Consider the following quedtions: Can they overload arbitrary key presses? Can they modify what is on the screen? Can they change the screen's content without changing the file's content? Can they call the editor's own editing functions? Can they be called by the editor's own editing functions?

Textmate can bind shell scripts to shortcuts, but letter keys always insert letters, and the editor always shows the file's content.

Emacs can execute arbitrary code on arbitrary keys, which enables you to implement vim-style key bindings. Also, Emacs can display stuff that is not a file, which enables mail clients, git clients, and terminal emulators.

Coming from the Emacs side of things, I will have to call that an incomplete understanding of the concept of extensibility.