Find somewhere where a YouTube video is already embedded (not YouTube.com) and do the right-clicking on it there.
YouTube videos started to go black for me a couple of days ago. No sound, no video, no loading, just blackness. I finally fixed it this morning by clearing all my cookies. Don’t know how or why that worked, but it did :eek:
It doesn’t even have to be YouTube. It can be any Flash object anywhere. Flash uses the same settings for objects.
And if you can get it to work there, try what Fear Itself did–a complete uninstall and then reinstall. You can even reinstall 10.1 from OldApps.com.
Windows updated today. Rebooted. All good now. 
That actually explains a lot. Rather than the bug being in Flash itself, it was a bug in Windows that the Flash designers didn’t know about.
Assuming, of course, that you had tried rebooting it before asking us for help. Things could have just gotten screwed up in memory.
NETA: Rebooting resets the memory.
Not in my case. Flash worked on other sites, just not on YouTube.
Second this. Flash even worked on YouTube, provided I didn’t click a link outside of YT which redirected to YT to watch a video. Embedded YT vids played just fine.
Bug in Windows? You don’t say. 