Most Helpful Guy
I would say this is a fair reaction. Your BF has every right to game, but he should devote time to just you, otherwise he's not worth your time. The key to sorting this is talking to him. Tell him that it really bothers you. If that doesn't work, you could try doing something similar when he calls you and isn't gaming. This just might make him see how you feel.
Most Helpful Girl
I dated a guy like this about a year ago. This sounds like him and you're probably the girl he was with before me and then ended up dumping me to get back with her. Does he suffer from bipolar? Is your name Kate?
No honestly. He clearly has an addiction. If you phone him or he phones you he shouldn't be gaming. If you're spending time with each other he shouldn't be either.
It's not gonna get any better. You're demanding more attention from him but he's just not going to give it to you. You could try asking him if he could call when he finishes the game or you call at a certain time when he won't be on. Problem is, gaming is not only addictive but concept of time is thrown out of the window. I get it's his hobby but if he's willing to throw away a relationship for the sake of an hour spent talking to you away from paying video games, then he's never going to put you first.
Get out whilst you can.