Kind of looked like it just sank to the bottom of the ocean like it was dead.

^^^ Yeah, it did. There looked like sediment was kicked up when it settled on the bottom.

Maybe it was just tired and wanted to take a nap.

Sperm whales are the deepest diving whales. Although they live at the surface they dive to hunt giant squid that are bottom dwellers. They have been known to dive as deep as 10,500 feet (3,200 m), but average dives are about 4,000 feet (1,200 m) deep. The Sperm whale can hold its breath for about an hour.

'Since water weighs 64 pounds per cubic foot, the underwater pressure on 1 square foot area will increase by 64 lbs every foot increase in depth'
(David Baxter & Timothy Schmidt: the Physics of Scuba Diving)

That makes it 185,600lbs per sq. ft pressure on that mammal. I wouldn't be dancing around, either. All the gas in it's lungs has been compressed into it's bloodstream at that depth, like a two ton Slim Jim. Not much wiggly left.

That makes sense. It is amazing that they were able to catch that on video completely at random.

Hmmm, 2 ton Slim Jim.
Sudden craving.

What kind of fighting tactics would a 2 ton Slim Jim employ aginst a bottom dwelling giant squid?

Play dead.