As quoted from the above video's description:

There is a new fad in pet care and on the surface it may sound good. But as is often the case, this fad is potentially harmful for your pets, is likely illegal, and misleads the public. It is called non-anesthetic dental scaling.

Only the most obvious deposits of tartar on the outer surfaces of the teeth get scraped using the above described procedure. The important areas where dental disease is truly located remain untreated.  These areas include crevices between the teeth, the inside surfaces (tongue side) of the teeth, and most importantly, the areas under the gums where dental DISEASE is actually located.  Further, the instruments used are sharp and can often result in painful injury if the animal suddenly moves. When the teeth are scraped, scratches and etch marks are left on the dental surfaces making plaque and calculus return all the faster because the dental surfaces are roughened. The "tickling" vibration and noise that occurs when teeth are polished is not tolerated by awake animals, yet polishing is necessary to smooth out any irregularities left after cleaning. Finally dental radiographs (X-rays) cannot be taken in an awake patient either because dogs and cats will not sit with a piece of X-ray film correctly positioned in their mouth for the exposure to be taken!   

While this may seem on the surface like a good approach to reduce the cost associated with dental prophylaxis, ultimately it does more harm to your pet and will result in additional costs ranging from a sooner dental prophylaxis needed because of the lack of polishing to repair of wounds caused by the instruments in the mouth.