I found a problem in Google Chrome and Microsoft Edge with HTML5 video in the mediaplugin. There is an attribute on the source-tag generated, called "type" and if it's set to video/quicktime it is not able to play the .MOV files. It works fine en Firefox.
A quick test confirms that the mime type is video/quicktime so everything points to a browser misinterpretation:
For testing instructions go to the issue: https://tracker.moodle.org/browse/MDL-73046