The short answer is that no one talks about RESTful websites because websites are RESTful by default. You really have to try to make a non-RESTful website (though it has been done--see below).
The setup you're describing takes a lot of elements from REST, but it's not "REST" per se: it's a set of conventions designed for the convenience of server-side programmers. Most of today's web APIs only use a subset of the REST constraints, and it's a subset that doesn't include the main driving principle behind websites.
Let me back up a bit. Here's what websites and web APIs have in common: they both expose functionality through resources. Each resource is identified by a URL, and each responds to an appropriate subset of the standard HTTP methods. (This may seem obvious, but look at XML-RPC or SOAP, where there's only one URL for the whole system.) A resource might send documents to the client (in response to a GET request) and/or it might accept documents from the client (along with a POST or PUT request).