There are two classes inside the .zip: Monitors.cls is the main control structure & procedures, while Monitor.cls is the object definition for the collection. Reading thru the code suggests it does not accept new values; it's just providing data about the video configuration. So in that regard it's not helpful, but still it might yield a clue. The API calls utilized are:
Basically upon initialization you end up with a collection of individual Monitor objects, one for each enumerated display. You can determine just about everything from individual height + width to the total desktop real estate available.
I did not include a referenced file, MonitorPickerForm, as it's a simple graphical display showing the orientation/position/size of each monitor object, similar to your screenshot but cheesier. Since you're not planning to compile this I figured it's not important.
Wish it was more,