Have you tried these steps:
1. Allow apps to be downloaded from anywhere from System Preferences.
2. Make sure to move the entire folder to the Applications section after extracting the .zip.
If that doesn't work, please let me know if you receive an error report, what it says, and what your OS is! Ren'Py officially supports Mac OS X 10.4+. If all this doesn't work, you can try using Wine to open the Windows version.