I believe that is the SMG barrel that has been modified to fit a semi-auto receiver. The semi-auto has a ring inside the receiver that prevents the standard barrel from fitting. Since the semi-auto ATF approved barrel is 16 inches, they had to modify the receiver to prevent the use of the 10 inch standard barrel which violates an illegal law.
The standard 10 inch Uzi barrel has a full locking ring around it as well as what I believe are alignment bumps on the barrel. The barrel you show has the half round lock ring of the semi-auto, and it looks like the rest of the barrel that fits into the receiver was turned down to fit into the semi-auto.
To legally use it, you would have to pay the $200 NFA blackmail fee with resulting paperwork and other stuff.