That's the world's worst explanation of potential energy.
The problem with this demonstration is that any time anything distorts its shape, entropy increases. Entropy is energy not available for doing work so the more entropy increases, the shittier the bounce.
In fact, the ideal bounce would involve a perfectly rigid sphere striking a perfectly rigid surface so that neither of them distorts at all. This is obviously impossible but there are some close approximations -- e.g. steel ball bearings striking a thick steel plate.
To understand this, imagine your ball is made of tiny balls (atoms) connected by springs (chemical bonds). When it hits the floor, the springs on the surface compress. This causes springs deeper into the material to compress and some of the energy of the bounce gets converted into random internal vibratory motion of the springs instead of bulk motion of the whole package. If instead the balls were connected with rigid rods, there could not be any internal vibratory motion and the ball would instantly leave the surface with exactly the same kinetic energy it had before (at least, assuming the floor is the same rigid structure).
The further you are from the instantaneous touch and reverse ideal, the worse the bounce is. So something that flattens out a lot, like a water balloon, is a very poor model for a good bounce.