Hmm...in a sense, shopping is kinda different. The girls just go
in there, try on clothes for a while, came out and can still talk
with the guys. Plus don't you guys get thrilled watching your gfs
all dressed up? 
But if a guy is gaming, if the gf tries to talk to him during the
game, he will feel distracted, and the game can go on for hours. So
in the end, ended up no interaction at all.
It is not about the amount of time spent with your loved one, it is
the quality. Even if you spend 6 hours with your bf in a gaming
place, but no communication at all, is dat really quality
time?
At least choose a game that both of you can play together,
something that both of you can talk about while playing rather than
just one person playing and the other person watching. If the girl
does the same thing to you, wouldn't you feel bored?
