The card says, “If no one has any Keepers in play, insert this card into the middle of the draw pile. Otherwise, all players with zero Keepers in play are eliminated.”

Does this mean that upon the first encounter of this card with no Keepers in play it is then placed in the middle of the draw pile? But the second encounter with no Keepers in play, all players are eliminated?

A: No, there is nothing different about encountering it a second time. There are only two possible conditions no matter when it comes up:

It gets played, and there are Keepers in play.
• Okay, everyone who does not have Keepers is eliminated.

It gets played, and nobody has Keepers:
• It would suck for everyone to get eliminated at once, so stick the card back into the middle of the deck. This might happen anywhere from zero to many times in one game if, by some weird coincidence, nobody has Keepers every time it gets played.