Here's an interesting example of what I've recently called a performative game: Audiopuzzler, created by Georgia Tech PhD student Nick Diakopoulos.

The idea is this: the game offers puzzles comprised of audio content from videos taken from YouTube or news feeds. The player has to listen to these snippets, transform them into text, and fit the pieces together. The result, Nick hopes, is an enjoyable experience that also creates time-stamped transcripts of video.

CAPTCHA creator Luis Von Ahn calls these "game with a purpose," a name I don't like for reasons explained in the article linked above. As Roger Travis noted, "performative" is a loaded term too, but I still think it suggests what these games do more transparently. I'm tempted to say that Audiopuzzler is more honest about its goals, but perhaps that's because I know too much about it.