The bottom video of a cat is unfortunate because the poor guy in the video is scared to death. You can tell by his voice and his heavy breathing. Best to stop, get big and get loud. Firing a couple of warning shots is a great idea, but backing up confuses the message to the lion. I like to swear at them in a loud voice, throw rocks, sticks, etc. Put down your phone and scare the freakin mtn lion away.
That's actually not a stalk--rather it's a defensive behavior protecting its cub from the person (cub is visible at the immediate start of the vid). The widespread forelimbs and the slaps pretty much gives it away--bears do the same thing when showing defensive behavior. I'd guess the retreat is due to the adult moving the person sufficiently far away from the cub that it felt that the cub was not in danger.
Are these opinions contradictory? When being confronted by a constantly approaching big cat, should one stop and be aggressive and attack with rocks, or move slowly away? Or is the person supposed to adjust his/her behavior by somehow figuring out whether that big cat is protecting young (perhaps unseen) as opposed to stalking the person for purposes of hunting attack?