According to someone on the video, the shark was first noticed by some children at the waters edge. Authorities were summed and they were able to quickly wrangle the alligator and move it off the beach.
The women taking the video was upset because there were no signs stating that alligators will, on very rare occasions, make an appearance in ocean waters near inlets. In almost all cases, the alligators get caught up in strong currents following a heavy rain and get washed out into the ocean. Salt water is not part of its normal habitat and the alligator's primary goal will be to find its way back to fresh (or brackish) water.
To my knowledge, there has never been a case of an alligator biting a human while it was in salt water.
The video was posted on Youtube by dant025 and is 2:06 in length. (CAUTION: Adult language)