This quote is probabaly the saddest in a realy sad thread:
So so so much is wrong with that statement and it's coming from a guy who is well respected on this forum; other people will listen to your view more readily than some posters.
There are loads of studies you can find online which have found gaming improves different aspects of cognitive function.
Please don't 'begrudge' your kids for playing games, it'll only make them feel bad or even resent you for not understanding why they play. If you take an interest in their games, ask them questions, what they're up to etc it'll make you closer, give you talking points and they'll want to talk to you to tell you what they've been up to in their game. If you have time to try and learn to play, nothing will make you closer than giving them a game of FIFA or doing multiplayer zombies with them on COD.
There's quite a lot of assumption in your response, I'm afraid.
I don't begrudge them playing games in the slightest. I just limit the time they spend doing it (and plenty of scientific studies back up my view on that aspect of it). After safari, FIFA14 is the most used app on my iPad - again, you've assumed that I don't get involved. I play it myself, as well as against the kids.
I'll never be encouraging them to play Call of Duty, or anything similar though, sorry.