Yes, Morph Age is compatible with the Mac OS 10.8.5. I've downloaded the latest package and it even runs on the OSX High Sierra 10.13.4 with the latest updates applied.
Download the ZIP files and then extract it. Double-click the file and it should start asking you to enter the registration code since it's not a free app.
If Mac shows an error that the package isn't verified, then simply go to Apple Logo > System Preferences > Security & Privacy > Allow apps downloaded from > Install Anyway.