@CaptainNapalm
My answer indeed illustrated that updating does afffect current games.
As long as both players do not use exactly the same version (current one is 2.5.22294), your games might encounter issues.
I just looked at your game in question and was able to download the savegame file.
After downloading I opened the file in the current TripleA-release (2.5.22294) without any issue.
Am I safe to update to the latest version, or will that affect my other current games?
It is always recommended to finish games with the version they have been started with. As updates might affect current games (see above answer).
Is there a fix, if one person updates, but not the other, mid-game?
Unfortunately not. That is why it is recommended that the players check everyone is up-to-date before starting their game.
You can safely install and run different versions of TripleA side by side. Just make sure you install them into different installation directories.