Having the same issue here. I tried watching youtube videos in incognito mode and it work. Eventually i found out that for some reason my Synchronization was turned on. I signed out of opera sync and it worked for me.
EDIT:
Issue reoccured. I just added youtube.com to the Opera's ad blocker exception list
Link to similar topic
https://forums.opera.com/topic/65434/a-strange-problem-on-youtube