I've downloaded the latest version from your site and tried it in my Vagrant box StefanScherer/windows_2016_docker which is a Server Core edition.
Even at installation time I get an error message, see first screenshot.
After starting Fiddler.exe I see another error. I don't have a chance to enter any GUI/Menus etc.
I should be very easy for you to replicate the problem using a Windows Server Core VM.
With Vagrant it is very simple.
vagrant init StefanScherer/windows_2016_docker
then in the cmd prompt install you latest Fiddler version.