I've always viewed the term "hardcore gamer" as a distinction for, quite simply, someone who really likes video games and spends a lot of time playing and maybe talking about them. It's kinda like when you refer to a "hardcore Zelda fan"... that's just a distinction for someone who really likes Zelda and plays and maybe talks about it a lot, right?
Aside from that though, I also view people who seem to have a "natural talent" for gaming as being hardcore gamers... you know, these are the gamers who (often because of their experience with games) can pick up a new game and essentially master it very, very quickly. Also, the gamers who tend to really take it seriously. You know, the people who get really involved in the politics of gaming (id est, the people who can essentially give speeches for why it was stupid for the Halo Reach update to remove reticle bloom), getting on forums and discussing "serious" gaming issues, etc. I have one friend in particular who fits those descriptions, and I told him that I consider him a hardcore gamer, but he denies it, even though he spends a huge amount of his time gaming. It's kind of a subjective distinction, I think.
As for me, I don't really think in terms of those kind of labels. I've been playing video games since I was 5 (sheesh, that's 17 years... where's the time gone?), and I would say I'm somewhat good at it (though most of the friends who I consider hardcore gamers are definitely much better than I am), and I really like video games more than most, but I would never really make the claim of being a hardcore gamer. If anyone asks me about gaming, I just say that I really love video games and it's one of my favorite hobbies, and if someone calls me a hardcore gamer, I just kinda shrug. lol