Seems to be using WebRTC, so presumably it's using STUN servers to do the NAT hole-punching. So not really "no server involvement". But I suppose that would be basically impossible on today's internet. Hopefully it's not also using TURN servers if STUN fails...
Assigning public IPv6 addresses to every device in your home just pushes the "deny" rule to a slightly different part of the network stack. We will still require something similar to STUN to get around firewall rules.