Do you think he might be depressed? The pressure on teenagers even at comprehensives is enormous I cant imagine what it is like at independent school.
The psychologists told you he was trying to escape, do you know what he is trying to escape from, is it gcse pressure? Are there any subjects he really finds hard which you could help with or get extra coaching? Try seeing the world from his pov. I have no idea what his step dad is like but perhaps he misses his real Dad? Have you talked to him about what is troubling him, even if you cant help he may need someone to listen.
None of this excuses violence btw, but you might find it more useful to try to get to,the reasons for the violence than to rush into going to the police, or banish all gaming.
Gaming is not the same as gambling - many boys spend hours gaming and it can be a good way to relax and escape from the real world temporarily. It is a way of socialising with other boys, and girls, with similar interests and pressures.
He needs to learn to manage his time but may need some help from you. Rewards work better than punishments, why not make a deal that he finishes homework each evening before logging on to the games, and goes to bed at reasonable time, then he can spend the rest of the time gaming. Offer a bribe for good grades at gcse. Whatever it takes. Focus on the behaviour you want to see rather than the bad stuff.
Also, if he is good at programming or art then the gaming could lead to a future career, so not all bad, but to get into,one of these careers he would probably need gcses so does need to knuckle down and do his best to pass a few of them.