[Digimaster]

Furthermore, Enable Fullscreen video has to be enabled (otherwise the video doesn't start automatically).

I think you have selected IE as browser, so it perform clicks to switch fullscreen mode. Autoplay is blocked by default in Chrome Browser. To enable it, click on the lock icon to the left of the website address, choose Site settings and change Sound from Automatic to Allow.
 

But there's another major issue: stopping the browser player and exit from Chrome leads to Kodi stopping to respond.

It there another instance of Chrome running in background? Can you upload kodi.log? 

Sure, here you go:

https://we.tl/t-fOKq5PqXAO