Not neccessarily true. If that's a grizzly bear they cannot climb. At all. Hard to tell though from the video if it's a young grizz or a brown phase of a black bear.
All bears climb.
Some more than others but they'll all out climb any normal human.
Saying that i suppose if you were an extremely talented climber and there was a rock wall near you i can't see many bears getting up a shear rock face.
You'd better be good though cause he'll be sat waiting at the bottom for your arms of legs to fatigue
If a bear wants you dead then unless your packing some serious fire power the only methods you have are.
1/ Bluff it out by noise and waving your arms around to look big
2/ If #1 doesn't work curl into a ball and play dead.