What allows a ball (squash ball) to roll and not bounce out of a corner? In squash, a ball may roll out of a corner with little or no visible bounce.
What allows a warm and bouncy rubber ball, being hit into a corner with great force, to roll and not bounce out?
Can a kids bouncy ball (i.e., a very bouncy rubber ball of similar size but not hollow) also roll out of a corner?
Question coming from a non-physicist!
 A: I tried this with a tennis ball myself and for this to happen it depends a lot on the direction the ball is spinning and how fast it is spinning.

I tried it both obliquely and straight ahead and when spun in the right way it would roll just like the squash ball in the video you linked. Which is a good thing so now we can simplify the scenario into a two-dimensional collision.

(Red arrow: Friction, Light grey arrow: contact force. Clockwise and anti-clockwise with reference to the diagram)
If you could try it yourself you would see that if you spun the ball anti-clock clockwise the ball would try to climb up the wall. This is because friction opposes the direction of spin and friction on the ball-wall interface has a direction pointing upwards.
How about when we spin it clockwise, as I have drawn in my diagram?
It now depends on how fast you spin the ball, If spun fast enough the frictional force dominates against the contact force or "rebounding force" pushing it up and the ball stays grounded and the contact force on the ball-wall interface and friction on the ball-ground interface changes its direction.
I've refrained from using terms like momentum and angular velocity for your simplicity. I simplified the problem as much as I can and most of what's happening is the same for the oblique collision in the video but the ball most probably spun along the direction of travel as there seems to be no resistance to its motion and friction would have two more components that just slow the ball and its rotation everything else should be the same.
