It seems that trying to build a hypermedia API in the spirit of hypermedia precludes someone actually designing an app with any particularity (themes, layouts, pages, certain requests/responses being valid/invalid, etc.), since it must be so general, the only client application that could qualify is the web browser itself - able to render any HTML document without actually knowing about the document semantically. Because having prior semantic knowledge of the API violates REST. Assuming that, are the 'apps' and APIs one would design then just hypermedia documents? Sounds like web 1.0. Not necessarily a bad thing, really, but REST seems too specific to be meaningful outside of websites, either that or I'm not imaginative enough.
I'm not sure what a 'hypermedia API' looks like that isn't just a web page or a functional equivalent thereof. It seems that either the WWW is the REST reference implementation or REST is simply the architecture of the WWW codified.