[fritsch]

I have started from scratch.

Wiped hard disk, installed Linux anew on my NUC6CAYH (this time Linux Mint 18.2 instead of Ubuntu 16.04, but I doubt it makes any difference in respect to the Kodi problem).
Installed the usual updates, blah. Then Kodi (from the team-xbmc ppa).

Out of the box, with Mint's kernel 4.8, videos in Kodi ran, but with tearing, absolutely unusable.

Then I installed Fritsch's kernel 4.13 rc7 (http://fritsch.fruehberger.net/kernel/) which didn't help in my previous Ubuntu installation.

And bam, all videos absolutely smooth, regardless of framerate!

Finally I'm happy, all is running well!

I absolutely don't know what was happening on my first installation. Could it have anything to do with the fact that I made the basic installation connected to an old 1920x1200 DVI monitor so that the X system got a bit confused (e.g. wrong configuration files remaining) when I finally connected it to my HDMI switch and the 1920x1080 projector??

Mint is not meant as basis for kodi. It's compositor (redirecting kodi output) and precise playback don't like each other. the rc7 kernel is not needed, you can use a final 4.13.x ubuntu mainline kernel as you want. Also the initial monitor has no influence on that - besides mint is hard coding it's refreshrate for the compositor.

In short: If you want perfect playback, don't use compositors or desktop distributions. For a desktop player I suggest mpv.