I've been in this exact situation before, and I love video games. I don't think this has anything to do with your bias - it's not the video games that are making you anxious/stressed, it's the feeling that you're in a bad relationship with someone who doesn't want to spend time with you.

My ex would spend 40 hours/week playing a game similar to League (in addition to working a 40 hours/week job), and he would also lie to me about it. We'd lose date reservations or end up not going to events because he couldn't leave the game or his ranking would suffer. And so on. We fought all the time about it, and I really thought that everything in our relationship would be magically resolved if he just stopped playing video games.

But the thing is that we just were not good together in a relationship, and I wasn't able to realize it at the time because I was blaming all of our problems on video games, when in reality the video games were a symptom of the fact that we'd stopped liking each other.

I honestly think you might want to go to therapy, but only to sort out your feelings and take responsibility for your own happiness. If he won't stop playing video games and you're unhappy because of it, you're wasting your life sitting around hoping that he'll stop. Don't spend your 20s being in a relationship with a guy who's more interested in spending time on a video game than with you.