I had the same issue just yesterday, but I was able to solve it. I was trying to fix a different problem, and Apple Support told me I had to uninstall iTunes, and all the other Apple programs on my PC, and then reinstall the newest version of iTunes. It didn't work. I got the same Windows Installer pop-up you did. There's a Windows 10 update issue that's the culprit(for me at least). Anyway, what I eventually did(and this was just a fluke how I did this) was to download iTunes 12.7.0.166 again, but instead of clicking run, or open, after the download like I did the previous times, I opened my Downloads folder and right-clicked on the iTunes download. Then I clicked 'Run As An Administrator' instead of 'Open'. It started the install process again, and this time it worked. It reinstalled the other Apple support programs as well(except Bonjour). It even fixed my original problem. I can't guarantee that it will work for you, but that's what I did.
1 reply
12.7 Install failure - required program failed to run