Why is this specific video on Youtube not playing sound on my Macbook Pro?
That's an interesting question! There's a pretty simple answer - there's only sound recorded onto the left channel.

You should first check your sound output settings and see if you have the balance set to the center. Go to System Preferences--> Sound--> Output tab. Then check your balance.
You can play around with dragging left or right and anyone can recreate the issue by dragging the Balance all the way to the "right" when playing that video.

If you have your sound output in the center on the Balance, then you should try playback of your audio through your internal speakers instead of through the HDMI connection to your display (or other sound output).
That way you can isolate if the problem with your Display itself or in its settings.

If you find the problem only happens on your external display, see if you can adjust the sound settings on it and see if there's different audio selections.