It is harder to define what is a hardcore game now as a lot of games are played online.
The easiest way to differentiate a hardcore game from a casual game, in my opinion, is the difficulty of the single player and the accessibility of the multiplayer. Lets use the FPS genre as an example:
In the 1990s and during the early 2000s, FPS games had a single player campaign with bosses that were difficult at the least and impossible on the highest difficulty settings. Doom 2 and Duke Nuke'em 3D had really hard bosses. Nowadays, series such as Bad Company and Modern Warfare do not have a endgame boss or bosses in the traditional sense. What they have are scenarios that are difficult at first, but a piece of cake the 2nd time around.
Concerning multiplayer, back when Unreal Tournament and the like was big, guns had recoil, there were no minimaps showing the location of the enemy player, and the concept of killstreak rewards and deathstreak rewards was not yet invented. All you had was your hand-to-eye coordination. To be good at multiplayer in a game such as Unreal Tournament, it took real skill in honing your hand-to-eye coordination in getting headshots.
Nowadays, game such as Modern Warfare 2 are built for ease of accessibility in order to sell more copies. Skill in Modern Warfare 2 comes down to knowing the maps and all the hiding places to camp. You get 3 to 5 kills, go to a hiding place, activate your killstreak to call in a harrier strike, get 3 to 5 more kills from the killstreak, go to another hiding place, activate your chopper gunner, and you have a running 10 man killstreak (at least half from the killstreak reward).
I am not saying that there are not Modern Warfare 2 players who could do just as good at Unreal Tournament. What I am pointing out is the obvious, FPS along the lines of Modern Warfare have built in accessibility to the point where it waters down the meaning of what it means to be good at an FPS.
Take out the killstreak and deathstreak rewards, put in weapons with recoil (MW 2 has very few weapons with recoil and sway), open up the maps to allow sniping and run-and-gunning playstyles, and then you will have an honest FPS where skill matters and is instantly recognized without being clouded by accusations of being a no skill camper.