Elisp APIs and your standard editing commands (which are of course the pieces of Elisp that happen to be bound to keypresses). The difference between this and ncurses/other TUIs is profound - as you said, typical TUIs are data silos, just painting characters on the screen. Whereas in Emacs, all the text on the screen is accessible for search, navigation, copying, and even modification.
Even saying "Elisp APIs" doesn't do it justice; Emacs follows the best traditions of Lisp Machines - you can inspect and modify software at runtime, and make it do what you want it to do, whether it wants it or not. If an Emacs mode (i.e. essentially an Emacs app) doesn't provide some functionality, you can add it either way. Want to use pretty third-party autocomplete like Helm for e-mail addresses in To: field in your Emacs mail client, and want it to pull suggestions from some arbitrary .org file you use as an address book? No problem at all. Few lines of code and it just works.
The downside is security. You need to trust everything you run, because as you say it's so open and inter-winded.