Yea, with the LAN version there's no specific checking.
Here's what you would want to do for a LAN game:
You'll download Demigod from Impulse when it ships. You'll have a directory like \program files\stardock games\demigod.
You would copy that onto a USB stick or whatever and then put it on the other machines on your LAN.
When they load up the game, they'll need to enter in the email address associated with your Impulse account and the CD key. Since it's on the LAN, they'll all be in the same IP range and we've instructed Impulse to accept that for Demigod.
Then you would select LAN and off you'd go.