This is one of those "it's not a bug, it's a feature" type things
CBL is on the right lines. When a "normal" program displays something, it's using the Windows GDI (Graphical Drawing Interface) so all the API calls to draw something on the screen effectively go through the operating system, hence you can do screen captures, print screen etc.
However, that approach is waaaay too slow for video, so that's displayed using DirectX - in brief this allows the application to get a pointer to the RAM on the graphics card, and directly set the pixels as required. As the OS isn't involved, which monitor the results are displayed on depends on the application, and
AFAIK, currently they all default to the laptop screen - unless that's selected off.
So, if you have a projector connected to the laptop (i.e. acting as a monitor) video can only be displayed on one screen at any one time. The black rectangles that should have the video inside them appear because the OS DOES know about the borders of the window.
Hope that helps