I run the app and Launcher comes up in the dock, but no windows appear.
I can manually run the game if I open the RebelGalaxy.app and then navigate to Contents/Resources/game/RebelGalaxy.app, but this does not permit me to change any settings.

Downloaded as: rebel_galaxy_2.4.0.7.dmg
main RebelGalaxy.app reports itself as 2.4.0.7 (1.062), the internal RebelGalaxy.app reports itself as 1.0
The game displays 1.062.

I've seen that it opens a window but it opens underneath all the other windows you have open. You might check to see if it's hiding there.