Streaming a section of video to an external display
This is probably off-topic, because the easiest way to achieve this is to use the tools already provided by your graphics card. 

Mirror your display, adjust the resolution of your screen to that of the window, and pan the screen until the desired area is displayed.

If you want to be able to select an arbitrary window to be mirrored, you need to add this functionality to your window manager, which is impossible on Windows (but should be doable for most Linux window managers).  If you want to do this with an app you're developing (or an open-source terminal), just use a second display.