The way I see it, gamers do exist, but they exist in the same way that cyclists and readers exist. Now I can ride a bike and read a book, but I don't devote my life to it nor does it define who I am. However, there are people who amass a collection of hundreds of books, read every chance they get and when it comes down to it they are a reader as it defines who they are. Same with cyclists, they know bikes inside and out, build custom ones, use them to travel places that could easily be driven to and generally devote all their time to bikes.
My problem with "gamer" is that the general public seems to think that if you own a video game system, you are a gamer. The entire concept of "gamer" defining somebody who devotes their life to video games with the intention to complete every one and get the highest score is tossed right out the window when "gamer" = "anybody who plays video games". Why not just say "i'm playing a video game" in the same way that you're "watching a movie" or "reading a book"? It's just another sedentary activity. Now if we're talking about Move, Kinect and Wii motion control games, you might as well be playing a game of football in the backyard. It's just another physical activity. The fact that it's done using a television and equipment doesn't move it into this "gamer" realm.
In my opinion, let those who want to embrace the term do so, but don't group every person who enjoys video games into one massive group.
Per a comment on Kotaku, here is somebody who embraces the term:
Ok i don't think i want the term gamer to go. For me being a gamer is my life! I work part time just so i can game more and if i'm at work i'm on kotaku all the time. I like being a gamer. What else would you call someone that devotes his life to games? And don't give me any of that sad nerd or sociopath bullshit because i have a very good reason to devote most of my life to me and not to some mindless job.
Now I disagree with the above, I think that actually does read like the life of a sad nerd. He clearly believes that he lives and works FOR the ability to play games. I go to work to support me and my girlfriend (she works too, but we both work to support each other) as well as to further my professional career. Video games are simply a benefit that comes with making a living. I'll boot up a console 4-5 times a week, but I don't think to myself "today I work to earn money for games, everything I do from 9-5 is done to support my love for video games and in turn supports me as a gamer." Hell, if anything I'm a designer. Went to school for it, get paid for it and spend a good deal of my time putting it into practice.