I like the comment in the video "could be brake dust." Haha, definitely not. What it does sound like is the brake dust shield rubbing on the rotor as the car moves. Have you checked it to see if it is contacting the rotor? Maybe a rock lodged between the shield and rotor?
If your diff was making that kind of sound, your car more than likely wouldn't be moving.. And if it actually ends up being the diff that is making that noise, changing the fluid in the 'new replacement diff' is probably what you should do.
Seriously though, check the dust shield for debris/warp.
"! First rule of Italian driving, that which is in your mirror is not important !"