I assume you're talking about Chapter 2. Chapter 1 worked fine for me.
The Mac download has 2 issues:
1) One of the files in the zip is corrupt. Contents/Resources/autorun/game/day_A00_1.rpa is corrupt. Unzip from the command line (launch terminal, "unzip <dmd.zip>"), since unzipping by double clicking in the finder aborts. Replace it with the same file from the PC version.
2) The app itself is loading the wrong python file, so dies when trying to run. The app runs Contents/MacOS/DMD, which then tries to find Contents/Resources/autorun/DMD.py. This doesn't exist, but the python file is called DMD.CH2.py. Right click on the app, select "Show Package Contents", drill down to Contents/Resources/autorun. Copy DMD.CH2.py to DMD.py, and DMD.CH2.sh to DMD.sh. Then the app will run.