Do I have to pay to "gift" an app that I already own?

no.

If you want someone else to have the app, that copy has to be paid for, just as if you wanted to give them a boxed copy from a normal retail store.

You can sync your library on their computer and they can just download it from there ... be careful though im not sure if it erases your stuff when you sync it to their computer

That would be illegal.