In some searching I found there's a Scrabble variant on Yahoo Games called Literati, but there's also an offline party game called Literati Challenge which sounds like what you're referring to.

A few differences between the challenges: in QQ you're confined to one sentence, you have a day to write it, and you aim to illustrate the meanings of the words. In Literati Challenge (from what I gather) you invent a story in seconds and you might not know the meanings of the words -- you score points by bluffing. Sounds very fun -- thanks for pointing it out!