I just updated the updated itch desktop app on my Windows 10 machine, and both Breeding Princesses and another game in the same system installed and loaded and ran fine with the music from the ZIP files it downloaded from the main page.
Have you updated the desktop app? If it still gives you problem, delete the game file and re-download (choose the ZIP version if you have a choice) and install it. If that still doesn't work, perhaps you might need to rip and reinstall the itch desktop client?