That would be a load balancer but is not integral to the working of kubernetes. I wouldn't consider kubernetes unless you have a need for autoscaling. It's a lot of overhead for such a limited use case.
You can front any three un-clustered nodes with a load balancer to the same effect
https://www.cloudflare.com/learning/performance/what-is-load-balancing/
https://docs.nginx.com/nginx/admin-guide/load-balancer/http-load-balancer/
I would start here. Most off the shelf proxies can do it. Once set up you'll just have your friends connect to the load balancer either via IP or dns hostname. For anything behind a residential connection I would recommend either tunneling out or setting up ddns (dynamic dns) as the IPs can change every few days. Take a look at load balancing strategies as well
For the game server you'll probably want failover instead, which most proxies can also provide. This is because a load balancer could route everyone to different instances. I would set up save syncs between the three nodes so that if your primary instance becomes unhealthy you can simply reconnect to the same address and the proxy will route you to the secondary node. Obviously requires healthchecks. When the primary node becomes healthy again new connections will be initiated there.
Both of these introduce latency because you are adding a network hop though. You could also look into dns failover (direct to each node) to avoid this