Try starting the refund process. Once that is accepted the purchaser can then attempt to get their refund. For you it only matters when the game gift was accepted.

If you just want the game removed without any refund at all thats pretty much guaranteed. I do not know how removals of gifted games are handled or if the purchaser can appeal the moment they're notified of the removal(if they're notified).

My worry is if they can't recieve a refund, do they get nothing at all? Or do they at least get the game back?

In the olden days the game would have gone back to their steam inventory as a gift so they can give it to someone else. Since you can't create game gifts in your inventory anymore I presume they just get the money or at least a notice so they can try to get a refund.

I don't think so. The only way to give a game back is part of the refund process. If you're not refund eligible then no.

Gifts aren't special. They don't have separate rules.