Hopefully this should work everywhere as the libs compiled with gcc are linked statically so there's no dependency on libstdc++ as a dyn lib, and as far as I can see Qt only needs system frameworks, which should be available on all systems, even without homebrew installed... I will try installing a pristine version of macos and test it there see if there's any missing lib (which should then be compiled statically, also)
btw, just to be 100% clear: you do need brew installed to compile the .app and .dmg, but it should run on any machine, even without brew. If not, please report which libs are missing for you (should appear in the crash report)