How does Imp Temple scale with multiple people and multiple discards?
It means once per turn. You can steal a single card once per turn.

It's hard to justify this beyond the wording of the card. The card says once per turn, so you can do it once per turn.

In your scenario, your player stole a card three times in a turn. That's not once per turn. Otherwise, it would say something along the lines of "one per turn for each opponent".

The ability refers to a singular card. "When you force an opponent to discard a card, put that card into your hand". If more than one card is discarded at once, you can choose which one to take, but you can't take more than one, because then you've done it more than once per turn.

The ability refers to a singular opponent. If more than one opponent discards, you can choose who to take from, but you can't take from more than one, because then you've done it more than once per turn.

For it to work on all discarded cards, it would say something along the lines of "Once per turn, when you force an opponent to discard any cards, put those cards into your hand instead." In your scenario, this would allow the player to get 2 cards from one of the opponents.

For it to work as your player believed, it would have to say "Once per turn, whenever you force any opponents to discard any cards, put those cards into your hand instead." Alternatively, it could just not have the once per turn limitation.