As far as I can tell, it's the real deal, Tani, if only for the fact that an "excited" Taningia has a severe lights fetish, which is what drew this individual to the ROV in the first place..... The only other big finned candidate that I could think of would be Thysanoteuthis rhombus, which has a very different set of arm pair lengths, compared to your namesake and doesn't match the video.
Awesome, thanks so much, Ob! There seems to be a paucity of Taningia danae vids online, other than that spectacular classic on the SeaWiFS site -- which isn't really a video, just a Java-enhanced still. So it was fantastic to find this relatively lengthy close-up on YouTube.
I wasn't aware that my glorious siblings were so attracted to lights.... I wonder what (if any) evolutionary advantage that "fetish" might carry. After all, a big glaring artificial light looks nothing like bioluminescence, so I don't see how it could be mistaken for either a potential mate or a predator. Interesting!
If anyone finds any more Taningia danae vids, please post the links.... would love to check 'em out.