This video of a swimming Tremoctopus or “blanket octopus” was shot in the Gulf of Mexico in 180 feet of water at Eugene Island South Addition Block 330 in October, 2008. The location is 100 miles from the Flower Garden Banks, close to Sweet Bank, on the outer continental shelf west of Mississippi Canyon. The video appears to be from an industrial ROV performing inspections on an oil rig.
The footage is real, but the species is unknown. The genus is characterized by extreme sexual dimorphism. Males are ~100 times smaller than females. A similar animal washed up on the beach near Miami, FL last Friday, apparently, and another in 1964, according to NOAA Fisheries Biologist Heather Balchowsky. Special thanks to James Wiseman for the information and Emma Hickerson, FGBNMS for the tip and the link.