To be fair: "text editors" really hadn't been invented "long before emacs". At the time (the early 1970's) editing text was a subject of much research and experimentation. Differing paradigms were being tried on new and exciting hardware (the glass tty). Screen editors, as they came to be known, were a brand new curiosity -- they were equally disruptive (if not more so) as the "web application" or "capacitive touchscreen interface" would be decades later.
And emacs was one of the very first screen editors. It invented lots of the stuff that would later seem "obvious".
So no: I think it's entirely appropriate to say that emacs was "invented" in the same way the browser was.
It's before my time, but my impression was that both TECO and EMACS originated as teletype line editors (as with ed and ex, the direct predecessors to vi), and were only later adapted to fancy new screen terminals. Am I mistaken?
I likewise was never a user. But the EMACS package of TECO macros was intended specifically to enable screen editting on terminals as I understand it (though surely there was overlap). Basically EMACS:TECO as vi:ex.
And emacs was one of the very first screen editors. It invented lots of the stuff that would later seem "obvious".
So no: I think it's entirely appropriate to say that emacs was "invented" in the same way the browser was.