What you're seeing is the result of centripetal acceleration or centrifugal force or whatever physicists feel like being pedantic about. As an engineer, all that matters is that there's a force which is pushing uniformly outwards on the wheel, which results in two types of stresses: radial stresses (which act normal to the surface of the wheel) and hoop stresses (which act tangent to the wheel). This is basically an analysis of a thin walled pressure vessel minus the longitudinal stresses.
The waterjet provides the rotational velocity which generates the centripetal acceleration, which creates the predominately hoop stresses in the wheel. These hoop stresses are orders of magnitude greater than the minor radial stresses, which are presumably what you're imagining changing the deformation mode. So changing to another method of force application won't change the end result: hoop stresses accumulate from rotation until the tensile forces exceed the strain limit for this (presumably hyperelastic) material.
TL;DR, the end result is the same because the global forces generated by the rotation are far greater than the local forces generated by the waterjet.
Angular momentum is a measure of an object's rotation around a point (#spin) 🌪️.
Centripetal force is the force that keeps an object moving in a circular path, always pointing towards the center (#holdingtight) 🎯.
One is about spinning momentum, the other about the force directing that spin.
In this example:
As you shoot the water jet at the skateboard wheel, you are continuously adding angular momentum to the wheel. This increases the wheel's rotational speed.
As the wheel spins faster and faster, the individual particles in the wheel experience a greater centripetal force, pulling them towards the center of the wheel's rotation. However, at the same time, due to the increased rotational speed, the particles also experience a greater centrifugal force (which is not a real force but an apparent force observed in a rotating reference frame), pushing them outwards.
At a certain point, this outward "force" (centrifugal effect) becomes too great for the material of the wheel to withstand, overcoming the cohesive forces holding the wheel together, and it starts to expand and eventually breaks.
This being said, I'm not sure if that's actually correct what I just wrote, so take it all with a grain of salt (as one should do anyway when reading something online...)
The way I think about it is that all the individual atoms of the wheel wants to move in a straight line. The only reason the wheel doesn't fall apart normally when it turns is that the material is strong enough to hold itself together. However as it spins faster and faster it requires more and more strength to keep itself together and at some point it moves so fast that the internal strength of the material is not strong enough to pull itself away from this straight line, which causes it to break.