There is lots of functionality you can't do without some kind of non-ordinary editor functionality. The table functionality comes to mind, as does the time management functionality. But, really org-mode's syntax is simple and close enough to MD that it's very easy to implement in other editors. There is a vim package and even an Intellij package. But I challenge you to start implementing the non-syntax parts in another editor and you will quickly see that there is a lot of it.

> I should be able to edit .org files [...] and then re-process the file.

You can. It's a plain text file; Emacs provides a "live" and highly interactive UI for it, but nothing prevents you editing elsewhere and invoking Emacs, in "batch" (i.e. UI-less pure language interpreter) mode if you like, to evaluate, export, or perform whatever other actions on the file. I do this all the time, albeit in an interactive Emacs, with Editorial on my phone and files synced in Dropbox.

There are also libraries in languages other than elisp which provide some export functionality; notably, Github uses org-ruby, I think it's called, to HTMLify org files for web UI rendering.

Well, you can edit it in any text editor. You just don't get the automatic formatting, coloring, table calculations and so on that all depend on elisp.