pdonley has already tested installing SDL, but that didn't help and it shouldn't be required to do that either. Remeber, the terminal is your friend. Now put Dominions3.app on your desktop and write these commands in your terminal!!!
cd ~/Desktop
Dominions3.app/Contents/MacOS/Dominions3 -dd
Nope, you should be using the teminal or shell or whatever that application is called. Do a "ls" (lists all files) too so you can see if Dominions3.app is in the same directory as you.