It is difficult to establish a successful relationship with a girl if you spend the majority of your free time playing video games. It almost seems like people who play video games for many hours a day plus work would not have enough time to even want to spend time with a girl. One way to keep a girlfriend if you like to play video games for many hours is to limit the amount of time spent playing video games.
I would try to play the games when the girlfriend is at work or busy doing something else. Another way is to find a girlfriend who loves playing video games just as much as you do. Therefore, you will have time for the girlfriend and for your video games.