Agreed w/ draftermatt, the guy needs to make a decision as to what his priorities are & if he can't make his GF one of
them then it's time to move on. Admittedly I'm a bit of a video game junkie, but there's a pause button & it's no effort
to acknowledge someone coming into the room. There's also the final option, the "OFF" button (it's just a game).
Have the talk, maybe he's just a little thick & doesn't realize he's hurting you.