This isn't just about REST APIs though, but about APIs in general. e.g. a "dosomething" package or class you add in an application, or as a stand-alone library. REST APIs are a tiny part of all APIs.

You're right that GUI's aren't completely analogous to commandline UIs or API UIs; every form of UI has its own strength, weaknesses, and different audiences. Treating APIs as exactly the same as GUIs would indeed be a mistake, but the main point is that they're something a user interfaces with: that is, they're a "user interface", and it's useful to think of it as such right from the start.