I'm going to make some assumptions. First, that your SS goes to public school where he is not a popular boy. Second, that he is typically insecure and that he escapes into Xbox. Third, that that is okay with his mother because it makes things easier for her. And fourth, that you see it as a laziness problem that you would like to solve because having an unpopular insecure escapist boy around makes you uncomfortable.

You know how in all the movies about teenagers in conflict with their parents the parties involved come to an understanding after they each take a turn in the other's shoes? Freaky Friday, Footloose, Back to the Future, To Sir With Love, Goodwill Hunting....

You want SS to stop playing Xbox and to do more active things but he lacks confidence so pressure to be active makes him escape further into Xbox. Instead of trying to draw him out to you, try going in to him.

Have you ever played Xbox? Maybe the thing to do is to ask SS if he will teach you how to play. Reach for him on his turf. It might be fun. Once you have a bond, ask him to do something mildly active with you. Extra points for finding something game related.