Eggman, by your definition, I'm one of those guys who casually plays "hardcore" games.
The way I see it, when most people talk about casual gamers, they are referring to people who do not play "hardcore" games. They are talking about people who play stuff like Wii sports, and Nintendogs, and all those other simplistic all ages type games. Hardcore gamers are the people who actually play games beyond the current trendy popular games, and are more into games than the average "I want to kill an hour or two playing this mindless addictive game" type people.
In fact, I describe myself as at least a semi-hardcore gamer. Sure, I don't play on any of the next gen consoles. The newest consoles I own are the Gamecube and the PS2. However, I've always been fascinated with finding the rarer gems. The games that are really worth playing, rather than playing all the games that
But to be perfectly honest, I prefer my games to have a more adult presentation. Sure, the Paper Mario games are fun, and I don't have a problem with how cartoonish they are, but my personal preference goes to games that have a more adult presentation. Legend of Dragoon, most Final Fantasy games from FF7 on, Eternal Darkness, every new FPS, and the list goes on.
I will admit that I am primarily a RPG gamer, so that obviously biases my preferences. However, I simply find that too many games that I hear about for the Wii are cartoonish, and seem to be aimed at everyone (and by that, I mean kids under 12, since the "everyone" ESRB rating usually only applies to games that likely only appeal to kids in that age category.)
I will admit, I haven't had much of a chance to play a Wii, and the only game I have played is smash brother brawl (which I'm somewhat disappointed in, really. The slower pace bothers me. A lot.) However, many of the games that Nintendo seems to be releasing (and the general marketing style for the Wii in general) seems to be heavily catered to the "all ages" group, which generally ends up including young kids and families.
Bitch all you want about my personal ideas about how games are, or my personal biases. I realize a number of them are probably baseless, but except for the occasional gem (Katamari Damacy, Paper Mario, etc.) nearly all the games I actually enjoy have an adult style to them.
(Hell, I've quit playing Mabinogi, in favour of Atlantica Online because Atlantica is more adult (graphically), incorporates strategy into it's battle system, and is much less targeted at the virtual life aspect and more targeted at hardcore gamers.)