The term “gamer” is widely used and yet it is not used properly. People are called “gamers” just because they spend hours playing the same game, and that is not being a “game.” To be considered a “gamer” you need to enjoy games, play them, but also you need to play a wide variety of games, not just one series, developer, or genre.
From RPGs, to RTS, to FPS, to Adventure, platform, puzzle solving, to sports and every in between is a part of the gaming world. It is just fine if you don’t like some kinds of games, I’m not a big sports game fan myself. But you should be aware of them, and even consider playing them once in a while; you just might find a game that you like!
The genre does not make a game, ever. What makes a game for me is not just graphics either. To make a game great, sure decent graphics helps, but what is important for me lies in the use of game play, characterization, able to spend hours playing, and story. If a game has a great story, I am guaranteed to play it through, and most likely buy it.
Ultimately, games are the same as any other median of communication, poems and plays of the Greeks, to stories and novels and in this age, within the last one hounded years we gained new forms, movies, television shows, and now games. A game is only a story that is told by our times. New elements are brought in that allow us to become more involved with the world. To experience this brand new way is what makes us “gamers,” and nothing else deserves the term.