HHO (in the video) is just hydrogen gas. It's probably one of the oldest and most oft repeated fuel efficiency myths out there.
It's not really a myth. You can get an engine to run on hydrogen, BMW sold a 745i a few years ago that was "hydrogen powered."
BUT
What nobody seems to take into account is the MASSIVE amount of energy required to turn water into hydrogen. Nothing is free, physics assures us of that.
Here's another discussion of the
whole hydrogen thing.