Actually the game does support backups in the Linux sense (its a game created on Linux then ported to Windows and Mac). It can be duplicated for the others.
There are various player-created backup routines. I did a file here that gives you a new icon to click that will back saves of all your games.
http://www.dom3minions.com/docs/SavingSavedGames.zip
it basically does this...
C:\WINDOWS\system32\xcopy.exe /yes savedgames oldsaves /i
Others have taken some of my hints and created ways for you to add it automatic backups to your Dom3 icon every time you end a turn using the postexec switch on Dom3. I also like to add features like "resume game" or changing the default settings I got tired of changing every time I made a game.