I figured out my issue. First, I opened the binary and found that it is a Nullsoft installer, not a MSI installer. That pointed me to the EventViewer to find the error messages. (The error message I had from MSI was an erroneous attempt on my part to get logging info.)
Once I found the logging info, the real error was this:
Access to C:\Users\{username}\AppData\Local\Temp\Fiddler4Setup.exe has been restricted by your Administrator by location with policy rule {70676551-f9f8-426f-acff-2efc50630cb0} placed on path C:\Users\{username}\AppData\Local\*\*.exe.
So I went to my Local Security Policy editor, Software Restriction Policies/Additional Rules node, and found the offending path which had "Disallowed" and I temporarily changed it to "Unrestricted". After installing I changed it back.