based on the gist of what I Love Bees and the NIN promotion was about, "reality puzzle game" is a better definition.
Somebody sets up a puzzle with real clues in the real world (items and web sites, etc) and then seeds those clues where people can find them.
the entire game takes place in the real world, and tends to be presented as "reality".
As opposed to a fantasy LARP, where what's IN game/character is pretty obvious.
Some time ago, I had an idea to create a sort of "spy" game for some friends, wherein they would undertake some spy-like operations (drop off stuff, surveliance) all done in public space (without the public being in on it. This might be a form of ARG.
I'd be curious to more explanation on what this Renegade game entails.