I don't agree with the video explanation. Decoupling the speaker from additional materials that can vibrate is a good thing, because the additional sound from the additional locations will muddy things up. (This is the "secondary resonance" Auralex is talking about.)
I don't think the SubDude results in more "energy" being allocated to moving the driver back and forth instead of moving your floor. If you assume the subwoofer box has enough mass and friction to prevent back and forth motion (spikes obviously help because friction is greatly increased) opposite to the driver motion, then that ensures the driver is the only thing moving. (Auralex does not make any such claim like this.)
The cabinet is then vibrating due to the air waves internally/externally and any little kinetic energy transfer passing from the driver through the rubber surround to the cabinet.
Auralex's product description does not make any claim of making more of the amp energy spent on the driver instead of vibration. I believe, and I think this is also Auralex's claim, that the subdude simply absorbs the kinetic energy and converts it to heat, instead of the floor receiving the kinetic energy and converting it to movement. (The amount of heat conversion being represented by their Impact STL graph.)
The claim about cabinets and dishes rattling is also wrong, because obviously your subwoofer should be powerful enough to make that happen just with sound waves!