So, is the little old lady who 'plays competition mah-jongg for blood' (I've seen this in real life - I can imagine it happens online as well) a gamer, or one who plays games? And if that makes her a 'gamer', then how do you acquire the relevant data?
Now that I'm not posting from the phone, the long answer...
Basically, I define a "gamer" as "anyone who honestly thinks they're a gamer", so long as they understand that it includes a level of passion for games beyond simply playing them. That mahjong-playing granny? If she thinks she has a passion for games and thinks the term "gamer" applies to her, then yeah, she's a gamer. Though I also like consortium's answer of a gamer being someone who specifically makes time to play games, as opposed to playing games when there's nothing else to do.
I know that makes it rather difficult to actually figure out what demographic of the population are gamers, but that's never really been my concern with posting this.
I suspect if you compared the number of gamers to people who play games vs the number of gearheads to people who own cars, you'd find "gearhead" is a much more specific, niche group.
Perhaps, and there might be need for our terminology to evolve and create terms for people that are "more hardcore" than others when it comes to games. That there's possibly a smaller distinction between "gamer" and "one who plays a few games" doesn't mean there is no distinction.
Honestly, the term "gamer," particularly when paired with the term "hardcore," is mostly just a way for some people to discriminate against/ignore anyone they feel doesn't share their interpretation of games these days. Ex: I talk about the balance of Guilty Gear XX's roster, someone disagrees with my position by arguing Potemkin is too OP with his myriad forms of frame invincibility, I disregard them by suggesting they wouldn't have a problem with Potemkin if they were a real gamer like I am - they just need to git gud/lrn2play. Scrub.
"Elitist" is also a term, and I think that's the one that should be used here. That some people misuse the term doesn't mean it loses all value.
As far as I'm concerned, if you have more than a passing interest in video games, you're relevant to this conversation. It doesn't require a passion for games or some deep enthusiasm for the culture. You just need to be relevant to the games market and, therefore, relevant to this discussion about the nature of games development, why they include the content they do to try to sell games and so on. People who play casual games only are just as relevant as people who mostly buy the latest CoD to spend hours calling other people degrading names online (and maybe occasionally shooting them). As Pumpkin Seeds rightly pointed out, there are people who play these "casual" games in a manner that puts some "hardcore" gamers to shame in terms of dedication and money spent. These are artificial lines people draw to separate themselves from people who don't enjoy games the same way they do; they are divisions that have no meaning.
Just because a game appeals to casuals doesn't mean someone can't be a gamer and still play it. If that casual game is their primary focus, that's fine, though if they didn't have a level of passion for it exceeding the average playerbase, I'd question their honesty in calling themselves a gamer. An example would be Hearthstone; it's very casual for a card game and I think it has a lot of appeal to people that aren't gamers, but if you were to try and tell me Trump isn't a gamer because he plays a casual game, I'd be questioning your line of thinking.
As for people relevant to the discussion, I apologize if my posts made it seem like I was insisting this was an issue "only for gamers"; that wasn't my intent, though poor wording on my part may have made it seem that way. My only intent was to question the usefulness of the "47% of people playing games are female" statistic.
If I had to use the term: if you enjoy playing games, you're a gamer. But I'd rather just not use it. It's almost never used in a way that adds to a discussion, at least not that I've seen.
Males are likely still the majority of the video game audience. They aren't, however, as dominant as some people would like to believe. Women are a major part of that audience, and the fact that they're brushed off as "casual gamers" often misses the point that the cause of this divide in preference of gaming content may have a lot to do with, y'know, the content of games.
I wouldn't say that anyone who enjoys playing games is a gamer, however - though if that's your criteria for someone being a gamer, then my criteria for being a gearhead is anyone who enjoys driving somewhere. Obviously, that doesn't apply, but if your definition of gamer is just anyone who enjoys games, then yeah, it's going to look like an overly-broad group. Perhaps it's simply that "gamer" is too similar to "game", and someone may not really question whether there's a difference between "gamer" and "person who plays games"; conversely, "gearhead" has enough connotation in just the name that even people who aren't familiar with car culture can easily grasp the idea that they're someone that takes cars a lot more seriously than someone who simply drives around in one.