Agree with all three answers from Ultee Khopree.
If you talk about modern video games such as Wii, you will find it hard to eat and play at the same time. The obesity is more from watching countless hours of TV with no exercise and binge-eating at the same time. A lot of people do it due to depression and others do it out of laziness. No-commercial channels such as HBO, Showtime and others makes it hard for an individual to do many things, let alone anything, other than watch the movie for the entire time.
Playing video games is good for the refreshment of the mind, it is less to cause obesity than watching TV.