I would maintain a high index of suspicion over this one. Lots of things that don't quite add up.

First off, they are drifting around aimlessly in a sailboat, why not raise the sails? Do they even know how to sail?

The motor quit? Did they start on such a long voyage with no tools or spare parts for the engine? Were they planning to motor the whole way? Seems a bit improbable. Carrying enough fuel to motor that far in that boat seems a bit problematic.

A years worth of food for both themselves and two dogs, a water maker, and lots of flares, but no EPIRB or SSB radio?

Over at Cruisers Forum there are some highly experienced sailors. Some have made the particular voyage in question. The old salts there (who actually know something about long distance cruising) are highly skeptical on their thread.

The whole thing smells very fishy to me (pun intended).

EDIT: More questions from the video:
A Force 11 storm on the first night, that lasted for 2 nights and 3 days? Whiskey Tango Foxtrot? That is one step below a hurricane. Should be easy to see if there were conditions like that on that date near Hawaii?

Didn't think they could survive another 24 hours? Really? They looked pretty healthy and well fed to me.

The boat was too big to get into Kiribati lagoon? Sounds pretty bogus to me.

Devils Triangle? Where boats go in but don't come out?

Cans don't work?

This whole story is just too weird for me.