On OSX Big Sur. I unzip crosscode-new-osx.zip, double click on CrossCode.app. I get a message:
You do not have permission to open the application "CrossCode.app"
it looks like ~/Contents/MacOS/nwjs is not executable. chmodding +x made it so and the app launches but then crashes. I suspect other files in the package have messed up permissions that did not get preserved via the zip?