I’ve begun to wonder about this question. There’s nothing implied in the existence of the fediverse that it will include every site, and there’s nothing implied in the existence of every non-fediverse site which would stop them from forming their own fediverse. One could technically say email providers have already achieved this, though this only really applies to email providers which doesn’t make it as useful as the fediverse we know and love. Are there actually other fediverses out there?
If a few servers are linked up and talk to each other using TCP/IP (?) but aren’t connected to the wider network, that’s not enough for it to be considered another internet (but it could be an intranet).
If a few instances are linked up and talk to each other using ActivityPub but aren’t connected to the wider network, I think that’s not enough for it to be considered another fediverse.