For me it works as browser app in both Firefox and Chrome, no browser extension required. As far as I'm aware the browser extension is only for launching the desktop app, which doesn't exist for Linux (although this help page implies it the extension is useful for Linux).
Note that there are also different WebEx versions around, depending if the main server from Cisco is used or some company hosted WebEx servers.
On a company WebEx I could login and start a meeting from Firefox, but the invite link doesn't work (it complained about Linux). I could join by manually going to the main page extracted from the invite link and then entering the meeting ID and meeting PW.
The invite link worked without issues on Solus with Chrome, so maybe try it with Chrome if FF doesn't work.
