Yes, the first web browser was WorldWideWeb. one of the first mail clients was /bin/mail. the first IRC client was irc. the first jabber server was jabberd.

And the first Matrix client was called Matrix Console. Much like all of the above, it sucked - it was a first generation thing I wrote in Angular on the Caltrain the day before we launched Matrix at TC Disrupt 2014.

So I'd say the analogy is pretty good. Riot (originally Vector) is a second gen client designed to make Matrix mass market - just like Netscape did for the Web. You can get away with the first crappy experiment being named after the protocol, but beyond that point it's just gauche.