It wasn't mentioned in the page, but I'm assuming the iPad version will need to be re-purchased even if I've already purchased for the PC?
I think so too. The App store has only limited functionality to give out licences outside the normal purchasing process (100 free keys, if this information is still correct.)
This is a constant problem for all Kickstarters which produces iOS apps.
(But seeing how I got the original game for 5$ and how much time I've spend with it, I am willing to pay again for it.)