H.W.
I think it was reasonable to request a 'family only' attendance for this event. As teens, we all had to learn-- it's really not about us, it's about others. This isn't about the girlfriend-- if he'd wanted to bring a gaming buddy, that wouldn't have been appropriate either. He's there to celebrate Grandma's birthday.
If he gripes, let him know that when he's old enough to have a fiance who wants to be 'family' and who will officially be family, she will be more than welcome. :)