It might be more than just a EULA. Often to sign up for an API key, you have to go through a bit more explicit agreement to a ToS than there is in a standard funnel. There's also a bit more of an expectation that people will actually read them (and are competent to understand them).
This extension doesn't use the API. It just injects some JavaScript. Just like every adblockers and password manager does.
It does not matter, he does not want to fight this.