Teamspeak (or ventrilo) used to be the way to go when I was into online multiplayer games (~10 years ago). Not in browser, but low latency and extremely low resource requirements (definitely less than one browser tab; we have tried Skype back then as well, but it was using too much recorded for the computers we had back then, especially if there was more than 2 people on the call). You could host teamspeak server yourself on your local LAN. Not sure if there is some easy discovery mechanism or you would need to know the local IP (and ideally set up static DHCP for the "server").

I imagine WebRTC might require some sort of server as well, so I don't think you can get something purely in browser on all machines, but if you learn about anything let me know!