I suppose that the definition of a "hardcore gamer" depends on your definition of "hardcore" itself. Dictionary.com [http://dictionary.reference.com/browse/hardcore?s=t] defines "hardcore" as "unswervingly committed", and I think that's a good basis for a start. Simply put, a hardcore gamer is someone who is "unswervingly committed" to the hobby of gaming. Note that there's no mention of the player's skill, or even the amount of time that the person spends playing any given game. I think that the number of people wanting to assign ego to the term "hardcore" has diluted it's meaning a bit. People wanting to pridefully declare themselves as "hardcore" because they're better at a game has caused the term to carry a lot of negative implications, but I don't think that it's necessarily fair to blame the term itself for that.
I am a hardcore gamer simply because it's my hobby of choice. When I get home from work I like to read about the latest gaming news. After reading the latest news I like to hop onto the forums to discuss the latest gaming trends. Once I've had my fill of talking about games, I'll fire-up whichever game happens to have my interest at the moment. When I'm done gaming, it's only because I'm either hungry or tired, at which point I'll go back to either gaming, or maybe reading the forums again. This isn't to say that I don't do other things; I check Facebook to see what the fam (and some friends) have been up to, I'll keep-up with the "real" news to some degree, and I have some other nerd hobbies I enjoy such as anime or tabletop games (though some would argue that counts as gaming, too). Over-all though, gaming is what I love.
More than anything, though, it's a bit of a personal term. It doesn't do any good to brag about whether or not you're hardcore because it shouldn't matter to anyone BUT you. Likewise, it doesn't do any good to call-out someone for NOT being hardcore because it shouldn't matter. If someone wants to think that they're hardcore, then go ahead and let them. If they're lying, it's only to themselves, and it shouldn't matter to do you either way. A casual fan of gaming's opinion on a matter is just as valid as a hardcore gamer's opinion.