> and that API must use hypertext
I'd say that my web browser is not using hypertext. It is merely transforming it so that I can use the resulting hypermedia, and thereby interface with the remote host. That is, my browser isn't the one that decides how to interface with the remote host; I am. The browser implements the hypertext protocol and presents me a user interface to the remote host.
Fielding might have a peculiar idea of what an "API" is, so that a "human + browser" is a programmatic application, but if that's what he says, then I think his ideas are just dumb and I shouldn't bother listening to him.
> Whether or not the API is being consumed by a script client or a browser client doesn't change the RESTful-ness of it
There's no way for a "script client" to use hypertext without implementing a fixed protocol on top of it, which is allegedly not-RESTful. Unless you count a search engine crawler as such a client, I guess, but that's secondary to the purpose of hypertext.