I'll have to admit here that I'm mostly an online gamer. I remember my mother thinking my brother and me were always alone, playing games in our rooms, never making friends. For me it was quite the opposite though. I could never make friends at school, as I was shy at first contact. In my online games though, I got to work past that and made many friends to talk to and even meet in real life! Heck, I even met my boyfriend during one of these games and we've been living together happily ever since! Depending on the game you might just learn some useful skills along the way aswell.
Ofcourse, there is still the benefit of family time while playing board games, which is also quite important! We played quite a bit of monopoly when I was younger, which was always a lot of fun. I think there should be some room for both forms of games :-)