I'm a gamer. I love games, I play since I was 14 years old (in year 2000). But, unless someone is a pro gamer, it is not normal to play for more than 2 hours per day on average. Sure, that can be rearranged so you play 4 or 5 hours for two days a week, then don't play for the rest of the week. Or, you can sometimes be on a vacation, have a lot of free time, and then you can play more than usual.

But, playing for several hours every day, and neglecting real life duties or people in your life is a path to ruin. I've seen stories about people, or seen some cases in real life, where people choose gaming over their partner, job or school, and it is so sad.

I think your boyfriend needs an ultimatum. It is either you or his games, because right now, you don't have a boyfriend. Why not make it official and find someone who will talk to you, go out with you and have sex with you?