I'm a little bit concerned about Itch giving me two updates on the files being changed, but the file sizes aren't different. Should I download V0.20d again?
This is a bug with Itch, I have no idea what causes it but don't worry, you have the correct version. It will probably fix itself when the next update comes out and it can re-write the version file.
If you can't be bothered to launch it from it's location in your files until then you can either:
A. Try "updating" the game, doesn't always work but it does sometimes
B. Uninstall and re-install the game (MAKE SURE TO BACKUP YOUR SAVES IF YOU DO THIS. They can be found at ...\cabin-by-the-lake\CabinByTheLake-0.20d-pc\game\saves By copying that "saves" folder somewhere you can safely uninstall and re-install the game without losing progress)