WebRTC can bust through NATs with STUN and provide a TURN proxy in case the NAT can't be busted through. STUN will generate a number of candidate addresses that

WebRTC can bust through NATs with STUN and provide a TURN proxy in case the NAT can't be busted through. STUN will generate a number of candidate addresses that may be tried for initiating WebRTC connection(s). These addresses may be exchanged through a third party or directly communicated between peers once a data connection is established. It looks like the addresses in the animation are generally the local host addresses of the machines you are connected to. Perhaps the site is just showing the first candidate in the list, or, intentionally picks the local name to allow for moderate privacy.