This is not happening to me as much on youtube as some users here are saying. Maybe once a week it happens on youtube in google chrome browser. Happens daily in Opera though but on a different video hosting site.
I use multiple browsers and have multiple tabs open at same time and my pc only goes to sleep mode when I'm not using it. It also is only off when it gets restarted once every week.
My issue with a random video playing which I did not start is:
I will be watching a chinese drama video on Iqiyi website at night on Opera and when the episode finishes I will stop the video (but leave the tab open). I will then start doing stuff in google chrome and put the pc to sleep when I go to sleep.
The following day after logging back into my pc I will be using chrome for youtube and various other browsers for other things (not video playback) and randomly the opera tab that had the video playing the day before will start playing again. I may have gone back to other tabs in the opera browser the next day but I definitely did not touch or click the iqiyi website tab in opera on the following day. This has even happened when I was not using my pc but it was still on and the iqiyi website in the opera tab will start video playback.
I'm thinking this may have to do with auto refresh built into chromium browsers? This does not happen to me in other browsers. Only Opera / chrome