> Where this kind of API design is useful is when there is a user with an agent (e.g. a browser or similar) who can navigate the API and interact with the different responses based on their media types and what the links are called.

It's also useful when you're programming a client that is not a web page!

You GET a thing, you dereference fields/paths in the returned representation, you construct a new URI, you perform an operation on it, and so on.

Consider a directory / database application. You can define a RESTful, HATEOAS API for it, write a single-page web application for it -or a non-SPA if you prefer-, and also write libraries and command-line interfaces to the same thing, all using roughly similar code that does what I described above. That's pretty neat. In the case of a non-SPA you can use pure HTML and not think that you're "dereferencing fields of the returned representation", but the user and the user-agent are still doing just that.