…In other cases where an Action is played, and the conditions are not right to do what it says, the Action is simply discarded without effect. Extinction doesn’t go into the discard when played, however, it is removed from the game. So should one put it in the discard pile, or take it out of the game, without having caused something to “go extinct”?

To review: the Extinction says to “Pick any Keeper in play on the table which represents something living. Take it out of the game permanently, along with [the Extinction] card.”

Playing the Extinction card under those conditions (no “living” Keepers in play) it would have no effect, and should be put into the discard pile (so it stays “in rotation” and might come up again) rather than being removed from the game by itself. Basically, it’s only removed from the game if it manages to make something go extinct.