Turns out my ISP is blocking port 8080. I switched to port 81 (ie. on my router, I forwarded port 81 to port 80) and everything started working outside the local network.
I have not tested this using the standalone app, but it turns out creating the CGI app was quite easy to do.
To save someone some future headaches, here are the steps to set up the web app and web server on Mac OS X:
1. In Real Studio, choose Build Settings from the Project menu.
2. Click the WEB tab.
3. Set BUILD TYPE as CGI.
4. Leave CHOOSE PORT AUTOMATICALLY checked.
5. Click OK to save these settings.
Build the application and place the newly created My Application
folder into the Sites folder (which is in your home folder). If there is no Sites folder, you should be able to just make a new folder and name it Sites.Start the Apache Web Server (on Mac OS X):
Simply follow these instructions: http://osxdaily.com/2012/09/02/start-apache-web-server-mac-os-x/
There is one minor omission in the instructions above.
sudo nano /etc/apache2/users/USERNAME.conf
If you remember to replace your short username every time USERNAME is referenced in these instructions (and don't make any typos), you should be up and running.
From outside your local network, you need to add port 81 to the url to run the app (ie. my_domain.com:81). On your local machine, you can just type 127.0.0.1 or localhost.
Hope this helps some other newbie trying to get started with launching their first web app.