Your definition of a casual game is actually slightly wrong, based on the industries definition.
A casual game is a game that you can easily step in and out of.
Games like Wii Sports and Kinect Sports do fall on the casual side of the isle. Any carting game would be an example of another. While it may not be fun to leave these games for competitive reasons, there is no reason why one can't bow out of the game. There is no loss of progression in the story.
Most RPGs, most FPS', most dedicated sports games, most adventure games, most platform games, etc have a story mode that is progressive where leaving the game means losing the progression in the story. These are considered hardcore games. Any game that requires you to complete a level or stage to progress the story is a hardcore game.
The online multi-player functionality of most hardcore games technically falls under casual gaming because there is no requirement for progression to complete the level. It's a matter of achievement and or community guidelines against rage quitting.
Rock Band and Guitar Hero have both a casual and hardcore experience, the former unlocked through progression of the latter.
