Actually, what the video shows is what happens when you don't give the shooter proper training before handing them the shotgun. My mother (who taught me to shoot) was 5'2" and 90 lbs. She had NO problem shooting any weapon she ever tried, from her 12-ga. Ithaca to her .44 Mag. Ruger, to shooting a friend's .460 Weatherby elephant rifle. Though she did admit that the .460 had more recoil than she would like to handle regularly!
Also, the pistol-grip 12-ga. is one of the dumber ideas ever invented. The 12-ga. shotgun does have significant recoil. It should always be fired with the stock firmly braced in the shoulder pocket.