I published an update to an unlisted game and said update hasn't taken. Approximately how long does it take for the game to update the online version?

I find that changing the version number expedites the process. (It pretty much instantly updates when I change the game's version. It might just be coincidence, but it always works for me.)

I have nothing to do with that part, but I would be surprised if the version number made any difference - though it is good practice to do it anyway. I have always found that the update is essentially instant.

Are you checking with a saved game? When a player does a save, it is your entire game that is saved, and when the player continues from a save, the entire game is loaded from that save. That means if you do an update, saved games are not updated.

Perhaps it would be better if 'resume' wasn't offered after an update?