Great news! There might be a problem with the macOS non-10.14 download, though, in that it actually contains binaries for 10.14 instead of older versions of macOS. I will elaborate…
I have macOS High Sierra 10.13.6, and I specifically downloaded the “macOS 10.11-10.13” version from the “CERN mirror” on the official KiCad OSX download page: https://www.kicad.org/download/macos/ – the filename is: kicad-unified-5.1.0.dmg, and its URL was: https://kicad-downloads.s3.cern.ch/osx/stable/kicad-unified-5.1.0.dmg
I opened the DMG and dragged (i.e. copied) the respective folders to Applications and Application Support, and then went into the Applications => KiCad folder, and the macOS finder shows that all of the apps (kicad, bitmap2component, pcbnew, etc) have a “stop sign” through them which indicates that the app cannot be run in this version of macOS.
Double-clicking (say) kicad yields this dialog box:
You can’t use this version of the application “kicad” with this version of macOS.
You have macOS 10.13.6. The application requires macOS 10.14 or later.
My guess is that either the download link goes to the same download as the 10.14-specific version (but with the wrong filename) or the official 5.1.0 release for 10.11-10.13 has been accidentally built with the wrong internal macOS manifest/flags.
I can see that others have been able to run older 5.0.x versions on macOS 10.13, so with any luck this is an easy fix 
Otherwise, thanks for the great work!
Regards,
Anton Maurovic
algofoogle