Kinect is of course a great sensor for that, and does offer some advantages in terms of posture, but in the end all you need is good enough software to decode an image to achieve the same thing. It's not that difficult with today's image recognition libraries and capabilites - I think Kinect just makes it easier for the developer even with that said hence it's attraction for this title.
How do you think existing webcams know I'm holding my hand out in a certain position to indicate activate / de-activate something? I've played with plenty of webcam based routines that do the same thing in principle - work out whether you are in a certain position or not.
So it's definately doeable. Will a webcam be as accurate as Kinect? Not sure, probably not quite unless the lighting was good and the resolution suitably good to allow for clear rendering of the body position image, but for the average joe swaying in their living room I can guarantee it can easily be accurate enough to deliver what is perceived by the player as the same experience (with the possible exception Kinect may be better in lower light due to the IR and skeletal tracking).
However - I do want to note the genius of the approach here. The issue with all motion control titles isn't the tech working when you do the right thing, but the glitches (shown to exist on Wii, Move and Kinect already) that occur when you don't.
For example as noted on another thread Kinect misreading your move and delivering the wrong punch or jump... or Move deciding you swung down when you didn't quite, Wii picking up a change of position as a swing of your bat... and so on.
But with Dance Central, you follow the game, not the other way around. If you don't do it right, then it's easy, no input issues the game just tells you that you didn't do it right.
Clearly this won't work for all titles, but I do think the approach is a small stroke of genius for this kind of title.
It just seems a lot more "magical" when you don't break the system down to analyse how it's actually working.
As you pointed out, Dance Central does not put the player in the position of the pupeteer for their onscreen dancer avatar; on the contrary, when the player plays, they are in fact the puppet, being fed input and cues by the program that tell the player what moves and positions to imitate and when.
None of the videos of Dance Central show the avatar copying the movements of the player, in particular "bad input" player flubs like missing a move, being out of step, wrong limb position, etc. They simply indicate the flub by showing a red aura around the character.
Now if there was a freestyle mode that allowed players to do their own moves to the beat, to include improvised moves not in the game's library of dance moves and steps, THAT would be incredibly impressive to see their onscreen avatar mirror those moves like a puppet in real time, as well as a pretty impressive bit of coding.
But unless I missed something huge, Dance Central doesn't do this. It tracks player movement, approximating limb/body position which it compares to the scripted routine of the avatar.
I think the main hurdle for using a regular web cam would be the lack of limb tracking as an outline only identifying algorithm would be far more error prone, not that it couldn't be done.