stIncMale
commented
3 years ago Looks like there is a much simpler solution, which is free up to five computers in the network (we only need two): Hamachi. Just in case, there is also https://www.zerotier.com/
Since we both have private IPs, we cannot communicate directly and need a third machine with a public IP, that we both can access. Maybe there are services that can be used to achieve such a connection, but if we do not find such a service, we may get a free Amazon Lightsail VPS (Virtual Private Server), and use a reverse proxy, e.g., frp to expose a server on one of our personal machines, or even simply run tic-tac-toe on VPS, when using it as a dedicated server.