If YOU want to quit video games, great, at least that's YOUR choice. But if you're doing it because she said you have to? Either find some compromise so you can play when she's not around or something. Or find a new girlfriend. There's no reason you should have to quit something you enjoy because someone told you to.
I'll also join in on the "dump her" wagon. But only if the following are False:
-You are addicted to video games like a crackhead is to crack. -You spend more on games than you earn in a month. -Game time interferes with family time. -Gaming effects your mood (rage, etc.) more than 1/2 minute after the rage moment occurred.
For the first, you need help, and selling your game stuff is a good idea. For the second, you need to have someone take possession of your plastic. For the third, you need self control. For the fourth, you (may) need therapy.
I did not discuss physical health (fat, skinny, etc.) simply because one can work-out and game-on simultaneously, if one does so smarter & not harder (like how one can jog on a treadmill & lose track of time watching TV simultaneously).
Now then, to the meat & 'taters.
If you are a gamer, but not ruled by said games as illustrated above, then there is (likely) nothing wrong that would cause your g/f to make you dump your stuff. If you had a model trail hobby, she would demand you dump it. If you were a coin collector, she would tell you to dump it. If you had a baseball card collection spanning back to your great-grandfather, she'd tell you to dump it. If you were secretly developing a Rosen-Einstein Bridge in your basement, she'd tell you to dump it.
She may have decided that she wants to stop her hobby. That means those closest to her must do the same as well, because she is right. It is a standard form of overarching manipulation and control. She wishes to mold her significant other into her mental ideal, rather take them as they are.
Now then, if it's an issue of health (like she quit gaming due to one of the four I listed above), then it is expected to be supportive and PACK IT AWAY. Don't sell, because if you were to break-up...you'd be left with nothing. Just as if you went on a diet, it is expected that she would eat the same, healthy meals as you to help support your goals.
When she speaks of selling your stuff, ask her "why?"
If it's an issue of she wants to to use the money to spend something on her (especially if she hints at rings), then forget it. You can save-up just as easily with or without your games. This is blatant & selfish manipulation, and needs to be stopped before it becomes a problem.
If it's an issue of "I want you to do this because it's something I want you to do (for me)" without a reason beyond "I gave up my hobby you need to do so now, too", then respectfully tell her, "Honey, I respect your decision to stop playing video games. However, this was your decision, not my own. I respectfully decline your request to drop my hobby as it is not affecting my health and it is not affecting our relationship. So long as you respect my choice to continue to game as I respect your decision not to, then whether I play video games or not will continue to not affect our relationship."