HTML videos not playing on Sierra 10.12.6
The first thing I'd probably do is start your Mac in Safe Mode and test to see if you can play videos fine? 

Boot into Safe Mode

Follow these steps to boot your Mac into Safe Mode:


Fully shut down your Mac
Restart your Mac
Immediately press the Shift key and keep it down 
Let go of the Shift key when you see the login window (NOTE: If you have FileVault enabled you may need to log in twice).
Take a note of what happens (i.e. can you play videos okay now?)
Exit Safe Mode by restarting your Mac as normal
Again, take a note of what happens (i.e. can you play videos okay now?)


Once you've booted into Safe Mode, let me know how you went and we'll go from there. Primarily we need to establish if everything works okay in Safe Mode or not. If so, we need to then establish whether videos can play okay when booting normally afterwards.