Downloaded, bought, registered, ran Transfer, selected transfer to iTunes. Downloaded iTunes, tried to transfer, was told to download iTunes. Repeatedly. Deleted both programs, tried gain. Repeatedly. I have a new computer with Windows 10.
The latest version listed on the official website is compatible with iTunes 12. The software is said to work with this version and according to the table that lists the system requirements, you can install it in Windows 10: Microsoft Windows XP (SP2 or later), Windows Vista, Windows 7, Windows 8, Windows 10.
I recommend downloading the latest version from website and try again. For iTunes and this app, make sure to run them as Administrator and everything should be just fine.