I think it's safe to say yes for all elastic (non-rigid) material.
I believe it depends on the elasticity. Deformation (Strain) occurs in pretty much every body because of the force you apply and it could be temporary at a macroscopic level due to the elasticity.
So an impulse results in a compression wave that propogate through the material.
Deformation also gives raise to the tranverse waves that you see in that clip, as the a compression on one axis affects the dimensions in other axes.
That is, what I believe, results in the wave-like pattern that you are talking about.
The dependent factor is elastic modulus. (Or stiffness: the extensive property)
It becomes permanent and can lead to structural failure depending on the intensity of the force and nature of the material; specifically the elasticity.
But yes, I think it's safe to say yes, to your question.
Interesting video showing compression waves in a spring: https://www.youtube.com/watch?v=ubRlaCCQfDk
Note: I guess the elasticity in the matrix is different to that of our world, given the extent to why the bodies deform.