I hate the term because it's usually used as a marketing tool (BRINGING THE GAME BACK TO THE GAMERS) or as some weird community term (Gamers are just normal people, yo!). It's an awful word because "game" is not really a verb: I don't game games, I play them. Even if it were an appropriate verb, nounifying verbs like that in general make me think of careers and other defining traits: Someone who practices law is a lawyer, someone who drums is a drummer, and someone who designs is a designer. The aspect of playing games is not nearly as defining to me as any of those words. I consider myself an avid fan of movies and music, but I don't have any job with those aside from partaking of them. Therefore, I would call myself a "music snob" or a "film aficionado", or similar words with less dedication. Perhaps if I was, say, a professional player of games I would call myself a gamer, but I am nowhere close. I play guitar, but I'm not nearly good enough to call myself a guitarist.
If the term is as vague as you describe, however, then just saying someone is a "gamer" means very little, in the same sense that saying someone is a "television viewer" or "instrument player" mean very little. It would need to be prefaced with some kind of narrowing adjective like "dedicated", "avid", or *shudder* something like "hardcore" or "casual".