You mean there exist online game that doesn’t have any host at the end point? So games like Phatasy Star Online runs on magic? I’m genuinely asking here.
So if you connect with modem, it isn’t multiplayer? If you connect third-party servers, it isn’t multiplayer? Connection doesn’t care what hardware is present at end point - all it care is that it satisfies authentication then following byte stream is correctly formatted. The fact that it is console doesn’t magically make it require different kind of infrastructure from PC to begin with unless someone forces to.
So what is definition of console multiplayer for you anyway? It clearly seems to be not “A session of a game where multiple players are involved locally or via internet” based on what you are saying so far.