Therapy is a good idea. The video games are not a part of the problem.
The problem is that he has had a very disconnected childhood with all the different homes involved and he has ADHD.
In fact, I would say from my experience on the ADHD forum
http://www.medhelp.org/forums/ADD---ADHD/show/175 that he is acting about the way I would expect him to given the circumstances.
Do you have any idea of what ADHD symptoms are and what an unmedicated child will do compared to a normal child?
And while medication is only part of an answer - all studies show that you need both medication and counseling. It may be part of the problem here.
Has his medication been changed at all in the last several year? Because it really sounds like it is not working very well. And it certainly is not working later in the day. They have medications now that will last all day long.
Let me know what he is taking and I can give you an idea if it might be in the ballpark of the proper dose or not (although all kids are different in how they respond).
I have many things that can help you help him. But it requires you learning about ADHD. The fact that you took the time to write such a long letter does show that you care very much.
I would start by buying the book, "The ADD/ ADHD Answer book," by Susan Ashley. About 10 bucks on Amazon. It covers discipline, school, etc. Just a a ton of really important information.
Then check out this site - http://www.help4adhd.org/en/about/what/WWK1 - a huge amount of very good info here.
Then for some parenting ideas go here - http://www.additudemag.com/topic/parenting-adhd-children/behavior-discipline.html you will find many, many useful ideas that will help you.
Finally, if you do have any questions about what you read or want more info post over on the ADHD site that I gave above and I will definitely see it and respond. Best wishes.