My opinion: saying that you like to play video games really has no place on your application. If it comes up in an interview, then maybe you could mention it, but it just doesn't really seem like the best face you want the admissions committee to see. At best, they could smile or chuckle and say, "Well, at least he's honest." and at worst, they could see you as having time-wasting hobbies and poor judgement for thinking that said hobbies are a positive reflection on yourself. I don't know why you'd want to take that risk. Nobody will look at that and think that it is unique or impressive. It couldn't possibly tip any scales in your favour, in my opinion, but it could tip them against you -- so why bother? I get that it's important to you and you think it's fun to do. That's cool. Do that! But your medical school application is not the place to write down everything that you do. It's not a Facebook profile, and you're not looking to make friends who share similar interests. It's about presenting information about yourself that makes you look like a great candidate to become a physician. Unless you really truly believe that video games are an essential part of your reasons for pursuing medicine, I don't know how it could have a place on your application.
Now, I do have a question for other people reading/responding/thinking about this. Would it be different to list "board games" or "card games" in a list of hobbies? Obviously, they would not be something that could be listed in their own spot, but perhaps as part of a larger hobby list (e.g. "Running, swimming, drawing, playing cards, reading"). I mean, it's a similar thing -- both are pastimes that take time and have no bearing on being a physician. But is there a particular stigma against video games? I know that, for me, if I hear that someone plays video games extensively, I immediately get an image in my head of a stereotyped "gamer". I try not to let that influence my opinion of someone of course, but it is an image that definitely exists. I don't really feel the same way about board or card games. It's interesting to consider. Thoughts?