The most obvious issue with the video is that the author has decided to go through the "ten dimensions".
The 'ten' figure he's using appears to correspond to the ten dimensions predicted by string theory (and he says as much at the end of Part II), but then goes on to try to relate all ten of these to some sort of extensions of the many worlds interpretation of quantum theory.
It's true that one can describe superpositions of possible states in an MWI universe ('multiverse') using higher dimensions (six, to be exact), but I don't recall them ever being suggested as being anything to do with the predicted extra dimensions that String theories have suggested.
The 10 dimensions predicted in String theory, if they do indeed exist, are thought to be either curled up, and thus invisible, or sitting out there in 'braneworld', existing, but not accessible to us, since hypothetically we may be stuck a 4-dimensional slice through the bulk called a 'brane'.
ICBW on this, of course. I'm sure someone who is more expert can crank out the maths if necessary.