My first boss at the uni would tease me about my Emacs usage, saying, “It’s an operating system with a text editor tacked on.” I just smiled and loaded up a game of snakes within my Emacs buffer and carried on hacking.
He's not wrong though - Emacs was meant to replace the MIT lisp-machine/symbolics interface and it does a magnificent work of it.
The things that Emacs allows one to accomplish is quite insane, though, as with all lisp-projects, it also seems to suffer from the "Lisp curse" (which is fine IMO).
The standard "great OS, needs decent editor" quip is just that -- a quip. If you look at the actual history of Emacs, you will see that the it was originally a collection of TECO macros. The first Lisp version was written by Dick Greenblatt for Multics -- it was not intended to be an operating system in its own right. The Lisp machines had Emacs versions of their own -- called EINE, ZWEI, and Zmacs. So Emacs was well-established on multiple operating systems before GNU Emacs even came along. You could say that the GNU system as a whole is intended to be a successor to ITS and the Lisp machine OS, but Stallman deliberately chose Unix as a basis because he wanted GNU to be popular and Unix was already widespread in 1983-1984.
In fact, GNU Emacs didn't even get some of its more powerful UI features until the 90s, after Lucid Emacs/XEmacs was developed by Lucid Inc. as a component of their Energize IDE -- they found GNU Emacs at the time to be inadequate from a UI standpoint, so they forked it and added the bits they needed. Most of those were implemented back into GNU Emacs, despite that Stallman thought that, for the most part, they weren't needed.
So no, Emacs wasn't designed to be a software Lisp-machine workstation. It just sort of slowly morphed into one over time.