I think it sounds likd your BF is not ready to have a serious relationship. IF he is, he would attempt to put some limits on his gaming so as to have more time for his girl. If he wanted to try reducing his time gaming, he could try strategies such as setting a timer for 2 hours or 3 hours or whatever time he decides is his limit, and when the timer goes off, he is done for the day with gaming. For example, maybe he could do gaming from 6-9 pm each night, and then turn off the computer for good. If he is not willing to consider solutions like that, then I don't think he wants to be in a relationship. You write about how you don't get to have sex anymore due to his gaming. But what about the other aspects of a relationship? Such as hanging out together, talking, going for a walk, going out to dinner? Those are important too. Perhaps you can make a list: the positive things you are getting out of the relationship and the negative things. Compare them and see what you think. In your post you didn't write anything positive about this guy, so it makes me wonder why you are with him?

Good luck.