Jitsi is very, very impressive. But their whole platform is also bound up with a lot of other tech in the stack. (jitsi-meet, jitsi-videobridge, jicofo and 'Prosody' (XMPP).
You hint at this being a downside, but (speaking as a Prosody developer) this is one of the things that makes Jitsi extremely powerful and flexible.
For example, Jitsi delegates authentication of users to Prosody. Prosody already has a bunch of authentication backends ( https://modules.prosody.im/type_auth ) and Jitsi benefits from these without needing to reinvent the wheel.
I've seen the Jitsi+Prosody combo integrated into many kinds of platforms. People also implement things like custom access control, logging, notifications and provisioning at this layer. These things would generally be harder to customize in a monolithic off-the-shelf system.
While the docs you point to are quite easy to follow, most of the "going further" is really not well documented...
But we are indeed integrating Jitsi into a game experience
here and its open-source stack is really nice to deal with (after many days needed to really understand it).