The specific application I have in mind is an annoying game that only supports LAN play through autodetection of other games on your local network, and it won't let you enter an IP address.
So, what I want to do is make it so that myself and two other friends in different locations appear to be on the same local network, so that the game is "fooled" into thinking it's just using local LAN to connect to my friends when it's actually going across the Internet.
I'm having trouble finding details on exactly how to do this, because most people want to do the exact opposite of what I'm trying. They want to make a local machine appear to be part of the public Internet. I'm trying to make a remote machine from outside the network appear to be part of the local network, and there doesn't seem to be as much information on doing that.