I don't think it all comes back to food choices. I think it all comes back to lifestyle, including food choices.
My oldest son (19) spends quite a bit of time playing video games. He's far from obese. He's actually in great shape, and was the captain of his high school gymnastics team last year. When ds1 isn't playing videogames, he's out "throwing a disc around" with some friends, or walking to and from school (15-20 minutes - uphill on the way there), or working out at home or the school gym...weights, pushups, chin-ups, stuff like that, or climbing/jumping anything he comes across. He does handstands and does cartwheels when hanging out with his friends. When he can fit it in, he's planning to go back to Tae Kwon Do, and also take some dance classes, and would love to take sword fighting lessons at a local place. He has tons of interests, and one of them is playing videogames. He eats a bit more candy than he should (works in a movie theatre, so he has easy access), but mostly eats a reasonably good diet. He recently decided that pop was a bad idea, so stopped drinking it on a regular basis. He didn't drink it growing up, but did go through a period when he drank a lot of it. He's not super interested in nutrition, but does pay attention to it. There are so many different factors going on here!
I am obese. I wasn't when I was younger. Part of the problem is that I spend too much time at the computer, but I've been in a fatigue/computing time cycle for a long time. I'm finally buidling up some energy, and cutting back on the computer. (I've been somewhat anemic for several years, among other things. I think four babies, a stillbirth, and four c-sections, all between ages 34 and 41, took it out of me in a BIG way.) I make some stupid choices. But, sitting at the computer is only one part of the picture.
When I was younger, I knew a guy who spent at least eight hours a day, frequently more than that, playing videogames. He also drank at least a Super Big Gulp a day. He was skinny as a rail...probably because he was always moving when he wasn't playing games - martial arts, cycling, walking, running, etc. etc.
People keep wanting to find "the" reason for the obesity epidemic. There isn't one reason. There are many contributing factors.