I'll say a hardcore game is a game that requires you to manage an entire galaxy, yet can bring down the fight to a one on one battle of ship vs ship (Sins of a Solar Empire = 4x lovin)

I think hardcore games are games that appeal only to a very select audience (the 'hardcore gamers' obviously), due to their difficulty and relatively not being very well known. Like most people have said, often hardcore games require you to put a fair amount of time into them; however in my opinion, this time can also be used to practice the game because of its difficulty, and doesn't necessarily have anything to do with the length or size of a game world. Usually the term 'hardcore game' seems to be used only for games that are actually good, but not 'mainstream'. Still, this doesn't have to mean that a game is totally underground: for example, while Super Mario Galaxy is obviously not hardcore to me, a game like Resident Evil 4 is quite hardcore IMO. It's quite difficult to play, appeals mostly to the 'hardcore gamer' (someone who puts a lot of time in games and games discussion on the net, like most people here on VGChartz) and not quite to the casual/children crowd, and requires/encourages you to spend a lot of time (replay value, unlockable features).
Summary:
Hardcore games:
-Are difficult.
-Are not 'mainstream'.
-Require a lot of time.
-Appeal mostly/only to the audience of dedicated gamers. (-------> are not mainstream)