Hi fellow penguin enjoyer.
Navigate to /home/<user>/.steam/steam/steamapps/compatdata
Here it's a guessing game as the numbers are pretty much random, but if you don't have that many games it should be easy.
In the right folder navigate to /pfx/drive_c/users/steamuser/AppData/Local
If it's the right folder you should see a VotV folder here.
Inside it in /Saved/SaveGames
Cheers!