To answer your questions:

What is the end game?  It is about power and control.  It'll end when the child thinks his mom (or dad) is the World's Best Parent and the other parent is a skank ho.  The child also has to refuse to see the so-called "skank ho" parent, even as an adult.

Is it a power thing or a revenge thing?  It is about power and control.  Some PASers will claim it is about revenge.  But it really isn't.

Trying to get more child support or cut visitation time?  Won’t make any difference.  It is about power and control.  It might be masked as that, “I want more child support,” or such but even if such a parent gets their demands met, they’ll move on to something else to raise the roof about.

If the split was over a decade ago, maybe they were teen parents, or they have since married with more kids how come they can't move on?  It is about power and control.  It is not about moving on at all.  It can be about fear too, of course, fear of losing the child, but every parent has this fear.  In PAS this type of fear has been twisted and weaponized beyond belief.

Is there anything that can stop alienation or mend the damage done?  No.  Many experts would disagree with me on this, but the reason why PAS is so prevalent, is because it does work.  Not enough people recognize it for what it is and many will automatically side with BM, regardless.  A professional can give you some suggestions, but they may or may not work.

Do kids ever realize that they have been manipulated by their "parent"?  They can, but it takes a strong, intelligent, thoughtful, child or adult to see through this and recognize it for what it is.  The child has to be able to sense: Something is just not right here.  But, to put it bluntly, most children, including adult children, would much rather hate their dad for life than admit that mom manipulated and controlled them and did not have their best interests at heart.  Bio-dads tend to be minimized in our society anyway, so it is much easier to write him off than have to admit to yourself that BM single-handedly destroyed any kind of relationship you could have had with your father.  Also, the mother-child bond is much stronger than the father-child one.  And, loyalty, no matter how misplaced, will almost always go to the mother vs. father, regardless of what others claim or have evidence for.  You could have court documents saying the judge stated BM was guilty of PAS, and the child will still believe BM’s version. 

My two cents.  I know a lot of experts like to say that PAS can or will backfire, but I’ve rarely heard of a step-child come running back to dad (and SM) as an adult, for example, and say, “I was so fooled.  I was so wrong.  Please forgive me.”  I have heard of it happening, but it is very rare.

I agree with ldvilen, it's about power and control. It's also a way to make the alienating parent feel special and boost their self-esteem. 

Finally, I think many alienators often have personality disorders where they have an insatiable need to prove that their ex is wrong in all ways and the most impactful way to do that is to try to turn the children against him/her. This can also be used as ammo to convert others to their cause that the ex is "all bad" (one of the characteristics of some personality disorders is black and white or all or nothing thinking). If the alienator can say to someone, "his/her children don't even like them" then, in the alienator's mind, clearly they have "proven" that their ex is a terrible person. 

My DH has asked a version of the last question several times. He'll often say to me, "when will the children be old enough that I can tell them the truth about all these things their mother has lied about?" I tell him that he'll never be able to do that, because they've been conditioned to believe that he is a liar who is just out to get BM. The only "evidence" they have to support this viewpoint is BM's word, but they have never questioned it. 

PAS is all about tearing other people down (DH family, new wife, other children, etc) Instead of celebrating someone else's happiness and success stories, BM feels the need to use parental alienation because she has nothing else to offer. This is the only thing that makes her feel better. She feels like she has more power and control if she can feed SD lies about her daughter's Dad and his family. Ex. "they aren't your real family" "your step mom is prettier than you" "your dad only likes spending time with _______" 

BM makes herself feel better, by hurting SD relationship with everyone else, but the kid is always the one that gets the brunt of everything. These kids usually have self-esteem and trust issues, Not to mention being put on an emotional rollercoaster that is "normalized." BM that participate in PAS usually can't function unless there is chaos, so they create it themselves. 

It isn't just BMs, although mostly.

Mu exH has alienated our oldest out of 3 daughters. He has done it all by the book. She is 17 and in the last 2.5 years I have seen her less than 10 times.

she does see it but her sisters 15 and 13 do.

its about power control and revenge. 

IDEVLIN nailed it.

Here is a link OP that may help you.

https://drcraigchildressblog.com/2015/11/03/diagnosis-of-parental-aliena...

It is not just BMs and it isn't even limited to only one parent or the other. BioDad's can be toxic PASing POS people just as can BMs.  PAS can even be perpetrated by people other than the actual parents. 

Which was the case with my SS's SpermClan. They were not even the CP family and they were committed to demonizing my wife and PASing my SS against his mom and I.

They were hell bent on taking custody from my then 16 & pregnant/teen mom future wife.   The Spermidiot didn't give a crap about my SS and never in his entire life expressed any interest nor did he make any effort to have much to do with his eldest of four all out of wedlock spawn by three different baby mamas. SpermGrandHag was incensed that my DW had rescued herself and her child from the toxic command and control of SpermGrandHag.  What made SpermGrandHag even more toxic was when my DW refused to surrender to the SpermClan's crap, took out a ton of supplemental school loans, got an attorney and went to war with SpermGrandHag 

IMHO the only way to deal with PASing POS scum is to go to war and make it clear that their crap will never be tolerated and will  cost them more pain and money than they will tolerate.  Like any war, a PAS war is a battle of wills.  The side with the commitment and will to win at all costs will win. The sad part is, the kid who is PASd against one of their parents is the one who is the true victim.  

When fighting a war against POS PAS-ers, the sound side of the conflict must focus on the wellbeing of the child while effectively fighting against the side hell bent of screwing the kid up.

what is the end game?

The end game is to ice out the other parent.. and their new SO if applicable.. ensure that they are the only "relevant" parent to the child.. 

Is it a power thing or a revenge thing?

I think it is usually mostly the power/control thing.  They want to be the end all be all to their child.. they don't want anyone else taking an ounce of that affection.. or attention.

Now... sometimes anger over a divorce may bring some factor of revenge or need to "win" over their EX too.

Trying to get more child support or cut visitation time?

While these are often the goals of each parent ( to maximize or minimize visitation to shift financial support payments).. they don't necessarily go hand in hand with the PAS.. but certainly the PAS'ing parent will want the financial support even if the child wants nothing to do with the other parent.

If the split was over a decade ago, maybe they were teen parents, or they have since married with more kids how come they can't move on?

MOving on is a funny thing.  Even if the current spouse had nothing to do with the split there can be loads of resentment if their EX appears to be thriving or doing better than the PAS'ing parent is.  "If he hadn't gotten me pregnant I would have been more successful".. "I should be the one living in that gorgeous house NOT her"  (even if they want nothing to do with their EX.. they want that success.

Is there anything that can stop alienation or mend the damage done? All parents can truly do is be there for their kids and try to keep lines of communication open and hope their kids are smart enough to see through some of the BS and be able to ward off some of the PAS'ing parent's tactics.

Do kids ever realize that they have been manipulated by their "parent"?  Yes... I think kids can see this sometimes.  My DH's EX was a bit of a PAS'ing parent.. nowhere near as bad as some on this site.. but she definitely made her kids "pay" for showing us attention/affection.  She even cut off my YSD's phone when she was 18 because she decided to go on a day trip with us.. last words her mom said that day were "well, you clearly love your father more than me".  (she unfriended her daughter.. thefull works.. but later turned it all back on).  So, for both my SD's.. I think they knew that their mother wasn't being fair about their dad.. but since he was NCP.. they had more to lose/risk by not being more on her side.. and minimizing what they said to their dad etc.

Both girls have dealt with this differently.. the older girl I feel equally resents her parents for the divorce and the fact that she was not the princess she should have been... but she tends to see life as unfair to her.  She has a tenuous relationship with mom and tends to gravitate to whichever parent can do more for her.  She is an adult.. and we dont' give her money.. but we have a nice beach place that she can come use.. so she is "nice" for that.

The younger girl has always been resolute that she wouldn't take sides.  She is an adult now too and has mentioned in the past that she hated having to be in the middle at times.. but she understands her mother can be "difficult" and she loves us in spite of her mother's attitude.. but she still does love her mother too.. she just refused to take sides.

So.. can kids see things for what they are? yes.. but there may be too much at stake for them to change things.  believe me.. when you have an unstable BM that makes your life hell after you spend a great weekend with dad.. you learn really quickly to not dwell on that.. and watch what you say and do.

And PAS is not limited to the divorced. My ex started in on our oldest the day she was born. Not exaggerating. I used to have photos of him (since destroyed) where he is holding our hours-old infant daughter in a posture suggesting a weird kind of couvade-envy. It was grotesque. He enlisted the "help" of our "friends" one of whom made the mistake of phoning me specifically to ask why I was abusing the kid.

He continued downhill. My every attempt at imposing order on our daughter's behavior was met with, " Don't be so mean to her! Come here to Daddy, darling, and I'll let you ... " He sat in her bedroom singing lullabies until she fell asleep well into her adolescence.

Man, I am slow on the uptake sometimes.  She was 15 when we finally divorced. He died some years ago. Our daughter is a grown woman now, and she still is not right. My relationship with her is pretty much where it's always been--in the toilet. The ex didn't do quite as thorough a job with our other two (did I mention I can be slow on the uptake?) but each of them is a hot mess in their own way.

So no, in my experience anyway, they never get over it, same as with any other variety of child abuse.

Haha, I'm wondering how old your kid is? If your child is ten years old, I'd suggest talking with your provider. The best method is installing a unique program where you take control of everything. If someone has 16-17 years old kids, there's no need to protect them already, and you know what I mean. The most protective stuff I have ever seen was on https://www.familyorbit.com/blog/message-and-call-tracker/ . Quite interesting, many parents already started using it. And they always know their kids' location.

What is the end game?

As others have said, it's about control. But it's about other things, too.

In my case, it's the kids' father in part but it's coming largely from my parents and siblings. Long story short, I walked away from an alcoholic, dysfunctional family as I didn't agree to play the scapegoat role anymore. Any attempt to talk it out and change things only showed me that the behavior would continue.

So, to alienate my children from me, turn them against me is about control; it's about punishing me for not playing the assigned role, punishing me for calling them out, punishing me for making waves.

It's about showing me that I will suffer if I don't do as I'm told. So it's about maintaining the alcoholic family system, about keeping everyone in their assigned roles so no one has to finally face that they're all part of a messed-up system and no one has to face their own behavior.
 

And on some level, conscious or unconscious, it's about proving to themselves that they are in the right. If my children continue to love me and see good in me, it might raise uncomfortable questions. If my children turn on me, then they can all say, "See, SHE is the problem because WE all get along just fine. SHE is the one everyone is turning against so SHE must be bad."

They can now convince themselves that they are perfect, good, and in the right. For a (guilty) ex-spouse playing this game--they can convince themselves that their gambling, cheating, drinking, or whatever, really isn't the problem, THEY really aren't the problem.

So parental alienation on some level really is about a person's need to bolster their view of themselves.

PAS also is not only perpetrated by Xs against each other.  Others can get into the game as well.

In our case the SpermIdiot was about as completely uninvolved as a parent can get short of total no contact with their kid.  He was more interested in sustaining his harem, expanding his brood of out of wedlock progeny with underage girls, and periodically calling my DW with the tearful  "Do you still love me? I miss my family." bullshit.

It is SpermGrandHag that was our particular PAS cross to bear.  Fortunately the SKid is smarter than she is, alone he is smarter than the entire multigenerational SpermClan combined. And, the shallow and polluted end of his gene pool is dominantly overridden by the rockstar genes he gets from him mom. And.... by being raised in a loving two parent marriage between individually successful equity life partners who raised him with both strong examples of a mother and woman, a father and man, and with clear standards of behavior and performance.  He also had the benefit of being part of a multigenerational successful family with strong examples of a GrandMother, GrandFather, Uncle, Aunt, and rockstar cousins.  He leaped right in makes our family name even better.  As does his mom.

The Hag would try to PAS him against his mom during SpermClan visitations.  At a young age he learned to smell her bullshit and as he grew up he learned to confidently smack her in the nose (figuratively of course) by calling her out directly for her bullshit. He did it respectfully but directly.  SpermGrandHag used to call DW howling when that happened.  When SS shut her shit down regarding his mom, she shifted to trying to PAS him against me. With the same extremely unpleasant results.

He learned at a young age to protect himself from picking up the stench of their manipulative crap.  As an adult, none of them try any of their historic crap with him. They have learned the outcome of those efforts will be extremely unpleasant for them.

That kids and good people suffer this crap is heartbreaking to me.

I am blessed and fortunate that we have been able to counter the crap.  That an NCP clan would even try PAS is incredible since the odds of success are about zero.

During all of that, and still, his mom and I advise him to love them even though he does not respect them, and to interface with them respectfully. Until their behavior tells him otherwise.

I have been telling DH for YEARS that BM is trying to turn SD against us. DH kept telling me that SD will eventually see through it, She'll see that we are good people. I told him that it doesn't actually ever work out that way, but he insisted. Fast forward about 11 years... Now SD has followed suit, makes up lies/manipulates situations to get her feelings hurt, and then tells DH that she wants to go  home, that she doens't think that she'll be visiting for a while (this has happened two summers in a row). She also left early on Thanksgiving Break, and now DH will have only seen her 3 times since early July, and I am BETTING that she'll come down with a mysterious sickness again during DH's Christmas visitation.

So in my case the Alienation against us was successful, and no, no matter how much DH tried, it didn't reverse. I think that maybe SD realized that she was being manipulated, but she's joined in on the manipulation. Heck, BM has told SD that DH's bone disease wasn't real, believed her 100% even though DH literally just had surgery to help it.

In some countries, also some states in America, PAS is considered abuse, and I believe it. Its screwing with the child's emotions and extorting them for YOUR benefit... that's emotional abuse... So yes, BM has abused SD for years, and now SD has learned that she can ALSO use her time with DH and her tears as a way to manipulate her father... so GREAT JOB BM, you turned SD into a disgusting person through all the PASing that you've done.