The incident took place at Ocean Creek Golf Course. The man was retrieving his ball from a water hazard. The 10-foot alligator pulled him into the pond and performed a series of "death rolls," which is a technique crocodilians use to rip pieces off of their prey.
The victim was taken to the Medical University of South Carolina. Wildlife workers killed the alligator and performed removed the man's arm from the animal's digestive tract. Reports are that doctors attempted to re-attach the arm, but it is unclear if they managed to do so successfully.
The video below shows an example of a (small) alligator doing a death roll.