EDIT: This problem now appears to be resolved. If you are still having problems, log out of Steam, exit the client and restart. I still can’t get Configure to work, but Story mode and all characters now work.
On launch day, 14th of April 2015, the PC version of Mortal Kombat X had widespread problems for many gamers due to their use of an experimental install system which is causing large chunks of content to go completely missing from the game.