They had a very long tow rope. So the skiing person was about 100 yards from the ship (so the prop eddies was probably not a problem)
The ship was moving and dragging the line and the skiing person was pulled up next to the rope in a ski boat (hanging from a ski pole outrigger) when he got near the rope he grabbed it and let go of the pole.
I agree that if not done properly it could be very dangerous but it was still pretty cool to watch.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013