The good news? There’s a nice alternative DVD player that will sidestep the entire issue and work perfectly with AirPlay!
Whatever the nuance here, it’s sure annoying and a lot of people have bumped into this limitation of DVD Player. The concept behind this is probably something to do with the definition of “broadcast” rights with a consumer DVD playback system according to some Byzantine MPAA regulation that Apple has to follow so as not to get in trouble with the big players in Hollywood.The fact that you can still plug in your TV directly via HDMI and watch a movie full screen (particularly easy if you have an HDMI plug on the Mac directly, as the latest generation sports) presumably falls under some other nuance of the law as that’s an alternative approach to having the DVD in your computer but the movie shown on the TV. You can see that’s the case because you can watch an iTunes movie via AirPlay without the slightest hiccup. There’s actually nothing broken in the configuration you specify, what you’re hitting is a built-in limitation of DVD Player that’s tied to digital rights management (DRM) requirements for the Apple DVD playback code.
