Every girlfriend I've had up to this point played games with me, infact thats how I met most of my girlfriends. But to keep on topic, I do on occasion but prefer to play games on my own unless it's coop.
Any girlfriend in the right mind would play games with their boyfriend at some point if they really liked the boyfriend. Ie. Lovers want to do things with each other.
Like how boyfriends go shopping with their girlfriends even though they feel terrible on the inside.
Then again, my girlfriend was a gamer before I met her~
We play... everything that I play. And I mean, everything.