I made the transition from gamer to musicer and drawer a while ago, with some booking on the side.
In all seriousness, what does calling yourself a gamer mean? Most people have played a game at least once in their lives, and I'm counting board games for this. More if you include games made from random props and imagination.
It's a form of entertainment like any other. Why should you consider a home console to be any more unusual than a DVD player or a cable box? Why are games so different from a collection of books, movies, or CD's?
No one is a gamer, and everyone is a gamer. Whichever your preferred entertainment is shouldn't label you.