Yes, that would be typical I think for dredging an anchor That was the consensus on this thread: Anchors - Poor Man's Tugboat In that case the anchor is kept on a short stay.
Basically dredging an anchor the bow lets out the appropriate amount of chain and then puts the brake on and leaves it.
What the ships were doing in the Med was dropping an anchor offshore and then paying out the chain as the ship comes in. The crew pays out chain at the appropriate rate needed to adjust the the ship’s head during the turn and subsequent mooring.
I’m no expert in this so take it with a grain of salt. If I was planning on doing it I’d take another look at the books.
As far as the video in the OP given that it was an emergency they might have just been dragging anchor with no heading control from the anchor.