Would this be applicable to fast hashes like WyHash and xxh3 or are those not using polynomials? Is this mainly for faster cryptographic hashes?

It is applicable to fast universal hashes like Poly1305 and Polymur (the latter of which I'm the author). However it's not clear to me whether this work improves over the state of the art for that purpose, see some questions here: https://www.reddit.com/r/programming/comments/1wbgcke/comput....

This purpose is however much easier/flexible than actual polynomial equivalence since the requirement here is only that the polynomial is injective, not identical.

WyHash and xxh3 do not have polynomial structures.