Hi, Sabine!
I can’t duplicate your problem here. I have the same system, however I’m still running 10.8.1.
Moving the video to external screen works well here.
What sort of codec is your video using?
Have you connected the display with a VGA, DVI or HDMI adapter?
What version of Quicktime are you using?
It could be any of these reasons, then again it might be an issue with 10.9, but first I would see if using another codec for your video might be the solution.
I’ll run through some tests this evening and see if I can find out anything.
Maybe you should also mail this to Steinberg Support. (To be found in your online user area under “My Support”) They are in general very responsive.