I hear people say as per Roy Feilding that REST is not just for web services. If so, what other systems/mechanisms/anything can use it?
Any system that has some type of access to the server, can even be an onboard system that has access to the API network
Any system that uses URIs to communicate information would be able to use REST.
Example: a theoretical database that fully follows REST rules.
Example resource "serverhost/database/table/1"
The REST interface is designed to be efficient for large-grain hypermedia data transfer -- Fielding, 2000.
REST is intended for long-lived network-based applications that span multiple organizations -- Fielding, 2008
The problem, of course, is that if that's what you need -- the web is sitting right there, so in most cases it's going to be more practical to adapt to the web as is, and perhaps extend it a little bit in a useful direction.
The alternative requires not only re-inventing the wheel, but also persuading the world to adopt the new standard and use it.