I had this issue as well, but someone had posted a solution for it. Turn on the developer menu in Safari and then in the Develop tab -> Experimental features -> VP9 SW decoder on battery - enable
This fixed it for me and YouTube videos immediately play. Supposedly it also turns on 1440p and 4K in YouTube, but haven't tried it yet.
This also fixed it for me (2015 12" Macbook), even though I'm not running on battery. Ah, betas.