Imagine if you were to try to get a heavy boat moving ahead just by pushing with your foot or whatever. It would take more force get the boat to slide ahead (or astern) than it would if you were to push the bow or stern to get the boat to pivot.
It takes more energy to get the entire boat moving than just to get the boat to pivot.
It takes less energy to turn a ship at speed than to stop one.
The very first line in the video in the OP is “Do you remember the movie Battleship?”. The narrator does say that in the movie that the Missouri is turning but in his demo later he talks about using the anchor to slow down without turning.
It’s an important point that the video misses. If the anchor of a large, heavy ship is dropped at high speed there are very large forces at play and thus little margin of error.
On the other hand if the anchor is used instead to assist in a turn the ship, forces are lower and there is a greater margin for error.
The energy of longitudinal vs yaw motion is also the principle behind anchoring with the wind on the beam.