As I understand the context menu, it seems it's referring to the AIR program when in focus.
Let's say my AIR program is not in focus, and I have another computer program up, with text.
I would Love to right click some text I highlighted in any other program, or on the desktop, and see the context menu appear with an option from my AIR App.
Is this possible?
You can have an installer install right-click menu items. On Windows these are generally called shell extensions.
Do some searching around for that. There's nothing internal to AIR that will do this automatically.