I voted yes but it's more complex than that, I think it was in Extra Credits where they nailed it, you don't call yourself a 'filmer' or 'film watcher', nor a 'TVer'. Gaming is something I do, I do it a lot. I also work, I also go to the gym, I also watch films and the news, I read several political magazines, I go to bars, I drive a lot. These things don't define me, they're a part of me but not the whole.
Calling me a gamer because it's one of the things I do, even if it's often, is just bizarre. I'm not a gamer, it's a lame and rapidly becoming nonsensical label. Who isn't nowadays? Most people play some games, even if we cut out the extremely casual side, Bejewelled/Farmville etc it's not like there's only a few people in the world with a console or gaming PC. It's a huge number of people and being labelled as a result of being part of that group is just weird, really weird.
I'm not a gamer any more than I am a gymer. I play games and I go to the gym, they are things I do. Not what I am.