The problem is caused because a specific version of the Visual C++ 2005 CRT dlls is missing, namely 8.0.50727.6195.
I actually found this thread when I encountered the problem on Windows 10. Fortunately I have a solution as well 🙂.
Version 8.0.50727.6195 is not included in "Microsoft Visual C++ 2005 Redistributable Package (x64)" or in the SP1 version,
but in "Microsoft Visual C++ 2005 Service Pack 1 Redistributable Package MFC Security Update":
https://www.microsoft.com/en-us/download/details.aspx?displaylang=en&id=26347
Install that & iTunes should work.
Hope that helps