Contest generally connotes a fixed length group activity with a single, or small and usually predefined set of winners. Game is really the correct term, IMHO, but it's still negatively associated with productivity, to the degree some people don't like to admit they play games, which is likely only true in their mind because of their overly constrained idea of what a game is.

We spend much of our childhood doing accelerated learning through play (games). There's no reason that can't continue into adulthood, except for it culturally being slightly unacceptable. That's really counter-productive.