And since I likewise couldn't find any information on how Minecraft handles single-player, paranoia ensues upon being informed that it also works by hosting a server. >_>
Don't worry too much about things using servers. People always equate servers to things operating across the internet (which, it's true, is a major use of them), but ultimately any program acting as a 'server' is simply listening for connections on a given port -
which doesn't necessarily mean it's listening out for them from the internet, or indeed any external source. It's perfectly plausible, and indeed common, for a server to be a
local server - which is, a program running on one machine that's listening out for connections on a port
from that very same machine.
That's how Minecraft, Starbound, and a few other games run naturally, whether you're playing them singleplayer or multiplayer - they effectively have one program* acting as a server and running the world, and one program* running as your client where you are the player. Your client connects to your server - they're both on the same machine, there's not necessarily any interaction with the wider internet (or network) involved at all, it's simply the way the program architecture's designed.
So, short version: don't get mislead into thinking the term 'server' only ever relates to networks and internets - it doesn't have to.
* Yes, for those of you who know of such things, I know that these technically aren't program-level distinctions, there aren't two separate applications running here in the majority of cases (dedicated servers aside). Allow me some attempt at brevity.