This doesnt actually work, but it makes you feel good for the effort.

Scratches and abrasions are micro or even macro deviations in the surface of the lens, which at one point was a smoothly polished common level surface. Removing a scratch or abrasion requires resurfacing the lens.

What this and other attempts like toothpaste, baking soda, polishing compound and others do is clean the surface. That's all they can do unless you use a micro polishing cloth, like a super fine emory cloth which will grind down the surface of your glasses. This latter approach will likely remove any coatings you may have on the surface and could alter the vision index of the lens if applied to heavily.

I've tried the author's method and several other methods with 2 different sets of glasses with unsuccessful scratch and abrasion removal results. At best, you will get, temporarily, highly polished, but not scratch removed results.