I agree that it should not work that way, but I was hoping that windowed mode would help you play in the mean time.
It you do a quick google it looks like several applications battle lid closing if they utilize directx - including VLC. I did not see any real solutions, just that it appears to be happening to multiple users hanging monitors off of laptops. I'm guessing that you are cloning your desktop?
You may want to make your external monitor the 2nd monitor (extend the display but set it as primary) and see if that helps. Maybe if the laptop monitor is the 2nd screen it will not cause the DX error.
It may help the dev team track it down w/o having to replicate themselves.