I've been labeled in many ways before. I don't really care what people call me. Gamer? Sure. Geek? Okay, knock yourself out.
I rarely use labels for people. Especially in regard to my self. Truth is, they're mostly used in everyday conversation as spiteful, ignorant over-stereotyping. Sometimes, people will proclaim with great volume and much pride that they are labeled in some way. Some people will group together with other people that are labeled similarly.
For example: There is a group here in Iceland, where I reside, that calls itself, "Freaks of Iceland". They like to dress up in cyberpunk-themed costumes and frequently huddle together in the nearest graveyard to where I live. They revel in the label "freak", wouldn't have it any other way. Of course, people laugh about this, and many people look down on the group. The one thing they all seem to have in common is this label; "freak".
Then there's the gamers, which seem to be just about as an exclusive a club. I'd argue that gamers would tend to have less in common with each other than the "freaks" I mentioned before, because what the hell is a gamer? Arguably, anyone who plays and takes an interest in video-games (I'm excluding the board-game, war-game, card-game what have you gamer from this post, in case anyone mentions that). The people who fit that description cover a vast spectrum of character- and personality-types.
In short, a group of random gamers will probably not be my choice of company for huddling around with in the local graveyard.
My point is: "Gamer", just like "Goth", "Freak", "Comic-Book Guy" and all those other potentially useful but mostly used-in-lieu of insult labels are pointless. When you shout out your favorite label of yourself, all I see you doing is trying to set yourself aside from the people around you.
In the end, isn't it better to set yourself apart from others by the way you think, rather than the way you look, or the things you do in your spare time?
Why continuously use "Gamer" as an identifier?
I've never had to apply a label to myself in order to talk to people about my interests, and I doubt anyone else really has to either.