In my opinion, there is no such thing as a hardcore game(or they are few and far between) only hardcore gamers. "Hardcore" to me means playing a game for long periods in each setting or many hours out of a week and/or playing games to achieve "completion." By this I mean finishing on the highest difficulty if an option exists, clearing/defeating all side-quests/missions/bosses/etc., collecting all items/weapons/costumes/etc., and so on. For games where there is no true ending, hardcore would be shooting for the highest possible level/score or setting up challenges(such as 4-line clears only in Tetris) for oneself.
By this definition any player can play any game in a hardcore fashion. But also any game can be played casually. Either by playing for a little while every so often, finishing on an easier difficulty, and/or rushing through to see the ending.
A hardcore game to me wouldn't have a difficulty selection, but it would be very hard throughout. There wouldn't be any optional side-quests or bosses because they would be forced upon the player. That's not to say the game couldn't have options, but it'd be more like branches the player could take where either branch offers similar challenges. Save points, if any, would likely be fairly separated(though checkpoints could prevent too much repeating in the case of game overs) to force longer sittings. A game like this would probably be pretty niche, because most of the gaming population simply doesn't want to play every game this way. It makes far more financial sense to make the hardcore aspects optional and grab a larger audience by opening the game to gamers that would play it casually.
EDIT: My second post in this thread reminded me that another way to play a game in a hardcore manner is to finish it while doing a minimal amount of certain things. For example: low-level games, no use of magic or abilities, skipping key items that make the game easier, and so on.
