RPGs Defined

For a while now, I've been thinking about a functional definition of RPGs. In essence, what makes an RPG different from a boardgame, or poker, or football? Will Hindmarch and Eric Lang brought the question up during one of my nights of drinking, and I was too befuddled at the time to answer it. After many, intermittent thoughts over the months, I've come to a definition:

A roleplaying game is a game in which:

A. One participant takes the role of a referee or "game master"

and

B. The game has no built-in end state. In other words, the rules don't explain how the game ends.

I think B is the key point, since it folds aspects of competition (or the lack thereof) neatly into a broader, much more easily tested case. It is also, I believe, the critical point that makes an RPG different from everything else.