A "gamer," if we follow the rules of English, should be a person who plays games to the exclusion of all else. If you use a word that fully defines you, leaving no room for extra interests or hobbies, what does it say about you? It immediately becomes something to defend, or qualify. You can say "I'm a gamer, but I also read books." That's a bit forced, and doesn't it sound strange? Why the need to define oneself by one's hobby anyway? In what context could one naturally use the word, except derisively? And the news media does exactly that. "Gamers are lined up to get their hands on the new Call of Duty video game." Interviews with over-excited youths with far-away stares ensue, encouraging every mother watching to say, "I'm glad that's not my baby out there."
The word "gamer" is regressive. It accepts the portrait of us painted by the mainstream news media, and every time I hear it or read it it actually makes me feel a little sick. I believe in this art form, and I believe in the people who make it. That's why I am so hard on this industry, because I believe that as great as it sometimes is, it can get better.
So play games, of course, but don't let the playing of games define you. Why would you ever really need to describe yourself as someone who plays games, anyway? Do you walk up to people and say "Yeah, I watch movies." Well, of course you do, everyone watches movies. If games are to become part of culture, shouldn't it be assumed that you play games? Shouldn't it be presumed that we all do? In first world nations, isn't the person who doesn't play games in the greater minority, when you factor in Facebook, Angry Birds, and the like? The folks who play these more casual games don't consider themselves gamers, because they don't think of playing games as a thing that defines them. They're just casually consuming entertainment. And frankly, they're right. They see "gamer" as a term that describes someone else - they just happen to play games, it doesn't define them. And in their way, they're being more progressive than we are, as a result.
If you want to call yourself a gamer, fine. I can't tell you what to do. But if you want to start changing the public perception of the game playing public, so that the definition includes everyone who plays games, I say it's time to retire the word "gamer."