I managed to get the game patched before but that was after numerous tries to get the auto-updater to work. I'm posting this as an archive so I don't lose this information.
64-bit
"C:\Users\username\AppData\Local\Microsoft\XLive\Updates\57520fa2\Content\setup.exe" /f "C:\Program Files (x86)\Steam\steamapps\common\mortal kombat arcade kollection"
32-bit
"C:\Users\username\AppData\Local\Microsoft \XLive\Updates\57520fa2\Content\setup.exe" /f "C:\Program Files\Steam\steamapps\common\mortal kombat arcade kollection"
This is a very helpful thread on that.
