The reason he has to cough up the money is: he has to post bond before he's allowed to appeal. So either he pays what he owes, or he puts up the money to ensure he pays after the appeal is overturned.
Ms. Carroll, unfortunately, won't see that money for probably another year, but at least she can rest assured that Trump is going to lose that appeal. Even if he becomes Supreme Dictator in November, that money is gone.