My Android (HTC J One) suddenly stopped playing videos when I clicked on Facebook links that went directly to a video. I could play videos from links to websites, but not from links to videos.
Here is how I fixed this problem.
I closed the Facebook app and opened the Youtube app. I noticed that the Youtube app didn’t open properly. I tried to delete the app by dragging it to the trash can, but it didn’t delete. However, when I opened the Youtube app again, it asked me which account I wanted to use. I chose a different account than the one I had been using. (I have several Gmail accounts.) Once I chose the new account, the app worked fine. I went back into Facebook and I was able to play Youtube videos again.
It happened again a few days later. I closed Facebook and opened the interface that shows me which apps are open by tapping the “home” key twice quickly. I closed the YouTube app by sliding it off the screen. Then, when I went into YouTube, it asked me some sort of question (I can’t remember now what it was) about some sort of new feature. I answered it and things were fine again after that. I think the problem is that the YouTube app is sending out messages of some sort, but the messages cannot be read when you open the app from inside Facebook. So you have to close the app and open it from the launcher to clear out whatever message is causing the problem.
Google, please fix this!