While tailhooks breaking off does happen, it is rare. The C-2 was very lucky. If the hook hadn't broken off right away, it may very well have slowed the plane down to the point where it could not have gotten airborne again and would have gone in the water.
USS Coral Sea (CV-43) was decommissioned 30 Apr 1990, 12-1/2 years before this episode. Coral Sea never had F-14s. She made her last 3 deployments with F/A-18a in her Air Wing. The ship shown was USS John C. Stennis (CVN-74).