Can you really play a game and watch a video at the same time? I couldn't... Anyway, just configure the setting in Windows to have dual monitors. Have a video playing in one monitor (ideally the secondary one), and open up the game (which will open on the primary one). Have the game set on the same resolution as the Windows desktop is set to and there will be no resizing of the secondary monitor. Then you can play your game and watch a video at the same time.
To setup dual monitors in Windows, right click the desktop and hit Properties. Assuming you have both monitors connected, hit the settings tab and you will see 1 blue monitor and 1 grayed out and probably smaller monitor. Click the grayed out one and check "Extend my Windows desktop onto this monitor." Hit apply and it should show up with something on it, change the resolution to whatever and hit ok. It will change the res and you are set.