That checkerboard image is the result of FairPlay, iTunes' DRM copyright protection & anti-piracy system.
In iTunes, if you try to take a screenshot or record the screen, you'll end up with a "censored" screen:

As you can see, I took a screenshot of Tron, a movie I bought just recently (that I love). This gray screen here is your checkerboard. This same thing will appear with screen recording, although you might get a message referring to High-Bandwidth Digital Copyright Protection (HDCP).
Currently, I have not figured out a way around this, but if you want to play your movies and TV shows from iTunes to a separate VGA/HDMI display, you're going to have to play them in SD quality, which is 480p. From there, you may be able to screenshot your video.
If you experiment around in iTunes and you find a working method to record/capture footage, a lot of people will love it.