Having watched the video, I revert to my experience of a number of years as 1st Mate and Chief Officer on ships four times the size of the Illustrious and can say that, as my duties were always on the forecastle during port operations, I have much experience in these matters.
As disclosed this was a new build on sea trials, and as such they would have tried the machinery in deep water to see if it was up to the job.
The video shows that the brake man was in full control until just after the second shackle but it then went downhill fast.
Judging by the size of the windlass, this was quite a large ship which had a windlass each side of the forecastle and this was obviously the Starboard one.
I note that the brake, although having a large control spindle, was hydraulically driven. I also see that there was a manual brake for the anchor gypsy, quite apart from the manual brake on the rope drum, but they seem to have forgotten that after the runaway. Could be the hydraulics failed.
The smoke from the brake during the first four shackles, apart from the rust etc. later on, indicated that the brake linings were on fire quite early. Fire means carbonisation of the brake linings. Carbon is an excellent lubricant, hence no braking effort and the cable ran out to the 'Bitter End' which is securely fastened to the after bulkhead of the chain locker to prevent total loss of the lot. I was unable to count after the 14th shackle due to the dust/rust etc.
The jumping of the chain is merely caused by the velocity of the chain links passing over the chain gypsy. If the chain velocity overtakes the capacity if the gypsy to hold it, the chain will jump the gypsy and run free, bouncing over the gypsy, to the bitter end.
I was the Chief Officer on a ship bound for Nauru in the Pacific, when a painting detail on the forecastle let go the claws and the bar stopper to paint them and then let go the brake without putting the aforementioned back. Result, an uncontrolled run out in several thousand fathoms of water and the chain jumped the gypsy. The windlass had insufficient power to pull the deadweight of the chain and 7.5 ton anchor back up so we had to do it in bits using the deck winches to help the windlass with wire ropes on the drum ends.
Oh Bliss, Oh Joy.
Cheers
John