So does your steam app say something along the lines of the game.exe file being damaged? That is most probably because steam is glitching about permission to move files around, but this is not important.
What is important that if you go into steam/steamapps/downloads folder, you will see a folder with random numbers for name, and there is the "damaged" game.exe file inside (if multiple folders are present, then check them until you find it).
Now, don't just go and straigth up launch the game from there, or try to coy it to the MONMUSU folder in steamapps/commons, as the first will ruin the whole file, and the second will not happen, as your pc will most probably think you don't have permission to mess around the file (even if you are the administrator).
What you want to do, is copying the file, somewhere away from the steamapps folder, and then doing the same with the whole MONMUSU folder in commons, then just putting te game.exe file inside this new MONMUSU folder. This should happen without any problems.

Got it? Nice! Now you can play the game by launching it from this copied game.exe file, and your progress should be safe and sound.
If the glitch happens again, just do the trick once more. If this method didn't work... well, then I can't help you. Sorry.