"Take over the world" means either one or more AIs have official sovereignty over most of the world, or that they effectively control important decisions. Humans may still have a voice on symbolic and minor subjets.

"keep humans as pets" means AI is generaly benevolent to humanity, not because they are designed to or needs it, but because either they think humans are cute and funny, either they consider unsavory to kill them all or let them starve.

This market will resolve to no if AI has wiped out humanity by the year 2100. If AI has wiped out humanity, the market resolution is on them.

This market will resolve to no if AI is still under control of humans.