1) Men escape to video games to relieve stress and to escape stress. If he works then he needs to wind down and this may be how he does it (which is not a good way IMO). If you stress him out then he is doing it to avoid you and the responsibilities of caring for his kids. No matter what you look at it though, video games are addicting and it can be used just like alcohol. So if this were the problem, you have to solve his stress.
2) YOU can't make the marriage work. It takes two to tango and he isn't doing his share. You can't MAKE him care either. All you can do is do things without him and isolate him to his gaming. Sure, you will be neglected and not have the bond you want, but you do not have any authority over him. And from the sounds of things, he doesn't have authority over himself either.
3) If it is REALLY bad, and if listening to your concerns sounds like nagging, tell him that you want to go to a couple's counselor and that if he doesn't go (refuses to) then you are ending the marriage and want a divorce. The couple's counselor will help you two deal with your problems and hopefully help him mature and assume his role as father.