I think the difference between such a service and tmux attach or screen -x is that if person A wants to share a terminal with person B and that person A is behi

I think the difference between such a service and tmux attach or screen -x is that if person A wants to share a terminal with person B and that person A is behind a firewall / NAT, it would be painful to do without some kind of proxy (this is mentioned in the linked page be the way). You have to trust the proxy though.