Firstly, OP's question didn't ask what a LAN game was nor does it imply an explanation is needed. You know that questioning whether or not the OP knows what he's asking is presumptive and might be seen as insulting, right?
I'm sure you probably meant to be informative but OP has a legitimate question (which is what brought me here) and we could stand to skip challenging OP's personal knowledge about the question's premise. OP wouldn't have asked a question about LAN games without some kind of understanding about it.
Secondly, a LAN game verses an "Internet" is a huge difference to anyone not privileged enough to have unlimited high-speed internet access. Over half of the world only has internet access through a mobile device. A quarter of homes in the U.S. still don't have high speed (more in most other countries). And, of those that do have high speed, many are not unlimited bandwidth but have to consider the cost of online activity. LAN games SHOULD allow a group of friends to play together without internet access. That's a big difference to a lot of people.
AndrewT, RAID186 is right. The "Refresh LAN" button populates with online games. It is not filtered to the local network. It should say something like "No LAN games detected."
For anyone else, I found a reddit thread, which suggests you have to apply a crack to the game to play LAN games. I haven't tried it nor do I recommend it. (Game cracks often have a virus.) But it does seem to answer my question: no, I can't create an offline game on my LAN.
Maybe someone should ask Paradox if they know what a LAN game is. LOL