True physical LAN play isn't working; it's using the internet

[duckweedseattle]

I live out in the boonies where online play isn't an option due to reeeeally slow internet. Think: dialup speeds of 5-25kps. (No, I'm not joking. I wish I was.) For this reason, we have a physical LAN setup with 3 PCs connected by ethernet cables via a non-wireless router. We use this setup to successfully play a lot of old-school games like UT2004, UT3, Serious Sam Classic, etc. Most newer games with LAN support work great too: Rising World, Blockland, Staxel, Terraria, 3079, Don't Starve Together, and many others.

I have purchased two copies of Serious Sam HD and set the multiplayer communication option to "LAN" on both copies. The joining PC can see the host's session and join it for cooperative play. So far, so good.

The problem is that the two PCs are communicating over the (super slow) internet--not the LAN. I can tell this due to the crazy-slow latency. I can also tell because it forces a disonnect if I turn off wireless on either PC. When supposedly connected by LAN, characters "jerk" all over the screen and appear to teleport. When I jump, I only see my character jump on the second PC monitor about one time in five. The latency is that bad. It's near-impossible to play cooperatively because it's difficult to even follow one another through the indoor levels due to all the "teleporting" and "disappearing." This just isn't a problem in the older version of the game; the physical LAN cables mean near-instant response and zero latency.

Is there a way to force this game to actually use the LAN?

And just to be clear: I'm not interested in playing split screen. I purchased a second copy (in a second Steam account) specifically for LAN play.

I've tried some basic troubleshooting. Firewall is disabled on both PCs. LAN is selected as the multiplayer communication method on both PCs. It's set up exactly how I set it up for all my other games that work well using the physical LAN... but it's clearly using wireless internet and ignoring the LAN.

Any suggestions are much appreciated!