Quicktime is the latest version. I unchecked the graphics processor option and bingo, it's working! I turned the option back on again and it is still working so I'm not sure why I experienced the original problem.
Thanks so much for your help.
This means that your Graphics card is not compatible with Lightroom
Please update its drivers and try again
I'm using Lightroom CC 2015.6.1 on a MacBook Pro with Retina display. I'm having the same problem, the slideshow won't run at all unless I constantly keep the mouse pointer moving.
I've tried it with both the GPU acceleration enabled and disabled. This bug has been present for over 1 year. There seems to be no problem when running the slideshow on the HDMI output to a 720p screen, but outputting over Airplay to an apple TV or to the internal retina display doesn't work.