The video game industry and culture is full of badly defined terms that we throw around all the time without realizing that everyone's definition is a little bit different - terms like 'hardcore', 'RPG', and, the one I'll be discussing in this article, 'gamer'.
So, looking at the definition of the word, a gamer is someone who plays games. Simple, right? But, like everything else, the reality is far more complicated. Language is defined by how it is used as least as much as where the term came from. I mean, would you call someone who reads books a 'reader'? (Or worse, a 'booker')
Gaming is unlike most (not all) other forms of media in that an entire culture has formed around it. I see the term 'gamer' as not saying that someone plays games, because that is so general as to be almost meaningless. Almost everyone plays games, even if it's just Angry Birds on their smartphone waiting in line for their morning coffee. A gamer is someone who would identify themselves as a gamer - video games become part of their identity, in much the same way that computers or comic books or whatever become part of the identity of a 'nerd' or 'geek' (two other ill-defined terms whose meaning has changed drastically in recent years).
A gamer, in my opinion, is someone who plays games as more than just a diversion, whether for competition, social interaction (Farmville doesn't count - there's no true interaction there), to hear an interesting story, or some other reason. I would say someone that just buys the latest Call of Duty, Madden, or WoW expansion isn't a gamer in the way I would use the word - a gamer is someone who enjoys games in general, not one game or series to the exclusion of all others.
In short, a gamer is someone who participates in the culture. A gamer is the kind of person who reads a review of something before they buy it, who is interested in new kinds of games, and who is willing to seriously discuss pros and cons of different games.
Of course, many people use other definitions, and the gaming culture that the term is associated with has many, many subcultures (such as the shooter fans, or people who play only MMOs). The key point, I think, is that they understand enough about the games to look at more than just the name or the popularity of something before playing it.
So that's my definition of a 'gamer'. Like I've said many times above, this is just my definition, and although I've tried to make it as definitive and concrete as I can, of course people disagree, and that's just fine. Evolving perceptions of words like these is how languages change.
P.S. I've got a lot of posts planned out, but I've been busy with finals and now holiday trips and things. Hopefully I'll have some semi-regular content pretty soon after break. The XCOM series is still happening at some point, and me and a few other people are planning on doing an Alpha Protocol Let's Play, so look forward to more information on those in a couple weeks!