Well, RSS is just a simple example: its domain is small. Which is why it's nice to talk about. If you need bigger and more powerful things, than stuff gets complicated.
> With RSS, the client doesn't need to know very much--only one method is supported (GET),
I should have said ATOM and ATOMpub; it has a slightly more complex edit/delete workflow as well.
> The IANA define some other generic link relations, but there seems to be a very big gap between generic link relations ("self", "back", and so forth), and application-specific link relations that are necessary for non-trivial apps.
Right. The idea is that you use app specific ones at first, then, as you find they're useful and stable, you make them a generic one.
> How is GutHub's API useful to hypermedia libraries?
This is backwards. It's more like "how are hypermedia libraries useful for implementing the GitHub API."