I've seen many, many relationships strained by the men liking games and the women resenting the games.
The key is balance. I personally think most relationships are best off when you spend 2-5 days a week (most weeks) actively involved in your significant other. That does not mean sitting at home watching TV where you are barely interacting. I mean 2-5 actual dates where you spend quality time together sharing in what both people in the relationship need for a good relationship.
But conversely, each person needs 2-5 days a week (most weeks) where they have time to themselves. The GF/wife can hang out with the girls, soak in the bathtub, read a book, or watch Oxygen. The BF/husband can hang out with the guys, play games, or watch sports.
If your particular relationship needs the 5 days a week together plan and you want to spend 5-6 days a week gaming, it is not going to work out. You may very well need to cut back on gaming. Don't eliminate it, moderation is the key.