When will the WolframNotebookEmbedder get a documented API?
Soon! We're working on polishing the last bits of its documentation.
Are there any other kinds of out-of-cloud notebook display things in the works? I'd enjoy being able to embed Mathematica 3D graphics inside web-pages and whatnot.
Rendering WL-based interactive content will probably always require some sort of "notebook", but a notebook could only contain a single cell and it could be completely transparent to the viewer that there's a notebook at play. You could put a 3D graphic into a notebook and style it in such a way that it appears as just the graphic, without any decoration around it.
If your question is about whether you need a "physical" cloud notebook (a cloud object) "backing" the embedding (which is the case now, and will still be the case with the initial version of the Wolfram Notebook Embedder library): We're thinking about adding an API such as
wolframcloud.com/render?url=...
where you could pass in a URL that serves a notebook, and it would return an HTML page, rendering that notebook on the fly. Maybe it could also take a content parameter in case you want to supply a literal Notebook (or Cell...) expression. But there are some major hurdles to be figured out with this still, so no promises.
If you're asking about something that doesn't use the cloud at all, then I don't have an answer.
