You place the mission file into your MPMissions folder.
Head on down to multiplayer, click new, LAN, then the mission and boom, started.
You are correct, it does not need MySQL, but I'm not sure if characters will save.
You will also need either Tunngle(The one I use) or Hamachi.
I'm gonna create a no-MySQL Tunngle server if you guys want to try it with me.
EDIT: To play it on LAN, you just need the mission file. That's it. Characters might not save but unknown is a genius and he probably figured out a way.
DaiZy Single-player Developer (AI Units)