Is the wording of Google's QC Supremacy valid? Quantum supremacy using a programmable superconducting processor was published today. Scott Aaronson posted a few weeks ago a post about this paper and it was clear we will see a Nature or Science paper soon. 

The abstract’s wording is less extravagant:


  This dramatic increase in speed compared to all known classical
  algorithms is an experimental realization of quantum
  supremacy for this specific computational task...



Isn't supremacy a well-defined concept in complexity theory?
Wouldn't Shor's algorithm be considered a QC supremacy?
How can we define supermacy unless it's provable that there is no classical algorithm to solve the problem faster on "traditional" supercomputer besides brute force?


Note: this is an amazing paper and I am seriously asking to understand if the wording of the paper is acceptable by the QC community.

Related: IBM’s response.
You should read the new post by Aaronson, but until then the short answers:


No.
If you can realize it in a real world machine, then it would (if no one finds a fast, classical algorithm until then).
You don't prove anything. It's a practical fact, like AI playing chess better than humans. If a chess genius is born, (s)he might win back the crown for humanity!