Hey there, this is something that doesn't get discussed very often, but I think it's important and actually an interesting thing to talk about.
Video games have also given me bad anxiety. It was interesting, because about a year and a half ago, I was having panic attacks often, then I started playing a video game (an addicting MMORPG), and I stopped having panic attacks, but overall it made my anxiety even worse than it was before. I became addicted and by the time I quit my anxiety was terrible. It's hard to completely relax because many video games stimulate your amygdala, which is also stimulated when you are ruminating on negative thoughts. People with anxiety have larger and very sensitive amygdalas already.
Some learning and problem solving type games might be good, but overall my opinion is video games are not good for anxiety. I know the suffering we go through on a daily basis, and that video games can provide an escape from it all, but its very easy to play in excess. I feel about 70% better from three months ago when I stopped playing video games altogether, and I can guarantee I wouldn't be feeling this good if I didn't quit.
Some people say that video games help to focus their mind on something. Well that's part of my point, because most of my progress in returning to a functional state was learning how to refocus my mind at any given point in time; however, video games can kind of be a crutch in lieu of learning how to refocus your mind even without any particular stimuli.
Part of my anxiety when playing video games (and I don't know if this is true for you) is that I feel like I shouldn't be playing them in the first place. Again, this is my personal opinion, but I felt like my life was wasting away while I was playing video games, so it created anxiety because we get anxiety when we are not happy with what is. I had a hard time coming off video games because it's a constant dopamine fix. Gamers try to refute this by saying, "oh but food and sex increase dopamine." This is true, but its unlikely for a person to binge on sex and food for as long as one can binge on gaming. I know people who game for 3-8 hours at a time, or more.
Anyway, I recently did sit down for 45 minutes and played a game a week ago, just to see how it felt, and it didn't heighten my anxiety levels at all really, probably because my overall anxiety is so much lower than it was 3 months ago when I played them constantly. But my conclusion at the time was that I need to substitute gaming for more relaxing and creative activities. And if you want to stimulate your brain, something like lumosity is a good substitute for games.
In summary, I would say that if you really feel like video games need to be a part of your life, then quit for a while and come back when your anxiety levels are lower overall. But my opinion is to substitute video games for other activities that are relaxing to you. If nothing else relaxes you then that's an even better reason to quit playing for now.