Download both FS-UAE-Launcher and FS-UAE and extract with the built-in Archiver tool in macOS (avoid a third-party one, since it might extract symlinks and permissions incorrectly):
FS-UAE-Launcher:
https://www.dropbox.com/s/ipbg7i9hh2...64.tar.xz?dl=1
FS-UAE:
https://fs-uae.net/files/FS-UAE/Stab..._x86-64.tar.xz
Move FS-UAE.app and FS-UAE-Launcher.app from the respective FS-UAE[-Launcher]/macOS/x86-64 directories to /Applications and delete the remaining extracted files.
(If the Launcher still won't start, please send new logs
)