Suppose Barren Glory triggers. Before its trigger resolves, an effect causes Barren Glory to leave the battlefield. Do I win the game? Specifically, I'm confused whether "no permanents other than" means that I need to control the Glory for the effect to happen.
You win the game. The trigger condition is only concerned with you controlling no other permanents (and no cards in hand of course). The fact that the Barren Glory is no longer on the battlefield will not prevent the ability from resolving.
Because for the trigger to be true the player must have no cards in hand. The ability has an intervening 'if' clause, so if the player has a card in their hand when the ability would resolve the 'if' condition is no longer true and the ability is removed from the stack.