Okay, it looks like it's become more complicated since the last time I posted instructions. (Thanks a lot, Apple.) I'll update the main page but also give the low-down here:
First, navigate to the directory where NeuraQuarium.app lives
Then run "chmod +x NeuraQuarium.app/Contents/MacOS/NeuraQuarium"
You should be able to try and run the app now but get a message saying it cannot be confirmed.
Now, open your System Preferences and select Security and Privacy.
There should be a section saying that NeuraQuarium couldn't be validated and give you an option to say "Open Anyway."
Once you've registered this exception, you should be able to run the .app normally.