Hmmm... Not sure what's wrong there, but it's not the speakers.
I don't use Flash on YouTube — I use the HTML5 player in Chrome, and on my MBA with that player I can hardly hear the audio on the internal speakers (since it's so deep, I don't think the speakers go that low).
I then watched your YouTube clip and the crackling and distortion was very audible.
I then tried in Safari and Firefox (which use Flash) and have the same horrible sound as you. But — the sound is equally distorted using a pair of (Sennheiser HD650) headphones. And the distortion disappears if you turn down the volume a bit within the Flash player. So it's not the speakers, but either Flash or some piece of software layer that Flash uses which the HTML5 player doesn't. Somewhere with Flash, some piece of software is boosting the volume digitally beyond 0db.
Might want to try Mavericks just for kicks. The final version is out now for developers.