Changing a desktop background is a simple registry change, but you should know that A- many users won’t appreciate messing with their registry beyond adding/removing you software…
And B- you have to be very Very careful when messing with the registry.
I’m not sure how close this is to the method you would use today.
But this is aroughly what you need your game to issue on the command.com (assuming Windows OS)
reg add "HKEY_CURRENT_USER\Control Panel\Desktop" /v Wallpaper /t REG_SZ /d PATHTOTHEIMAGETOUSE /f
then
RUNDLL32.EXE user32.dll,UpdatePerUserSystemParameters