well i'm a 27 yr old aspie with ptsd, anxiety, etc, and i'v played video games (pc and gaming system) all my life, i first started playing the atari (gosh thats old, then the nintendo, then so on the playstation 2. and of course computer games as well. I think you really need to understand that your child who has autism/aspergers has very narrow interests. The only thing that i really want to do is play games/web design, or youtube right now (i play games 12 hours a day, i take a few 30 minute walks (leave my game running) . when i was in school, and younger i still played games for 2-3 hours a day, and would have to get my homework done and was even involved in sports.
But if your childs interests are only video games, and do not like sports. and doesnt want to do anything else, then don't restrict his time, cause he can learn quite a bit in a game. like cordination, problem solving, like what the other people have mentioned. Of course it's different when your an adult and you cant keep a job now (overworked, and completely shutdown and meltdowns) Just remember that best thing to do is if your child is stressed out, have him play video games or watch his favorite youtube music videos.
Anyway i am on disability now, and the only thing i can do is play games, to tired and do not have the energy too really do anything else. (if i didnt have video games, i would probably sleep all day and night and only get up to eat something, and or probably would do the worse you could imagine, which it's not something i want to mention here, cause i dont wanna scare parents. ... . Just remember you want to have your child do something that he loves, if it's video games, then let him do video games, without time limits.