Sure you can game in moderation, but if you do so you won't be a gamer. I think I average maybe a handful of hours a month playing games, and that is as much as I will ever see myself caring to spend on them. There is no way for me to relate to people who call themselves gamers.
I'm not sure what preconceptions you have about "gamers" are, but from what I know, most gamers are in their 30's and have lives outside of video games.
I wouldn't call myself a "gamer", as per your definition, but I've loved playing video games since the early 80's, which might not register with your experience. I'm an ordinary guy with a beautiful wife and kids. Not sure what your beef is.
I'll play video-games on occasion but to be able to pass myself off in that sort of gamer culture is I think impossible unless you are willing to glue yourself to a television for hours and hours a week.
Other types of "frats" do not need that level of dedication I think.