Ok. I tried the plugin with a different 3.9.2 WP installation and it works perfectly.
BTW – the proper code is being generated by the plugin.
It appears that my current theme is messing things up with video.js itself. as a manual hardcoded instance of a video.js video doesn’t work in my current theme either.
I temporarily switched to a different theme and video.js was working again. So the problem isn’t the plugin, it’s my theme. Why it was working fine two days ago and not today who knows.