Without a device sending and receiving data, you have no LAN. Cables and switches alone can't be a LAN. A router...maybe but still not really a LAN, no real data can be generated and passed between routers, only routing data, which is only related to the routing of the data generated by devices on a LAN.
A LAN could be any 2 devices connected via local cabling (presumably within the same building), with or without switches or hubs, which pass data between each other for the sharing of information.
Oh yeah, and for some games you can make one of the computers be the host (i.e., the server), so you could have the remote computer simply connect to the IP of that computer for connection to the game. Doesn't require VPN.