I ran into the issue of cinematics not playing in Battle for Dazar’alor. Tried without addons as well (by resetting and walking into a fresh raid with none on). Might be just a bug though, and nothing fixable from my end.
Hey! I have same issue with cinematics in Battle for Dazar´Alor. Fresh install of whole game and no result.
Deadly Boss Mod and few other addons have built in option to cancel every cinematic if possible, check this out, disable addon and it should work for ya.
A very good tip! I do remember this causing some trouble back in Northrend (during the Wrath of the Lich King expansion). 
Addons can cause some odd issues at times, do try without any addons installed (clear your UI (addons) completely) to see if that clears up this issue for you.
Have a few seconds to spare? Let me know how I’m doing!
Hey! Thanks for the suggestion. I did a full UI reset including uninstalling my twitch app but it did not fix the problem. There is still no cinematics