The guy in the video doesn’t provide a very detailed explanation. For a swinging action, the slowing of the lead arm is caused by a properly timed kinematic sequence in the downswing (not by purposely trying to slow the arms down).
In the downswing , the pelvis rotates first, then thorax (chest) , arms, club.
The pelvis moves first, then there is potentially some transfer of energy from the pelvis to thorax , then from thorax to arm, then arm to club via the wrist joint. As well as some energy being transferred through each segment , there are muscle contractions within each segment that can add to their movement,
When the pelvis transfers energy to the thorax , the pelvis will slow down while the thorax speeds up.
When the thorax transfers energy to the lead arm, the thorax will slow down while the lead arm speeds up.
When the lead arm transfers energy to the club , the lead arm will slow down while the club speeds up.
Here is a good analogy
A father is running with his child on his shoulders , then the child jumps forward off his fathers shoulders. What do you think happens?
The child is now moving faster than when he was on his fathers shoulders, while the father has slowed down because the child pushed him backwards.
The same thing happens in the golf swing:
The rotation of the pelvis is carrying the thorax/arms/club at the start, then the thorax pushes off the pelvis , then the arms push off the thorax, then as the club releases it pushes off the lead arm.
The added movements of each segment are caused by the contraction of the muscles that can move/rotate each body segment.
The pelvis is moved/rotated by using the legs to push against the ground plus there are pelvic girdle rotator muscles that can be contracted to help in its rotation.
The thorax is moved/rotated by the contraction of the internal/external oblique muscles.
The arms are moved by the shoulder girdle muscles.
The total affect of the above creates the necessary forces on the club via the hands to speed it up, but as it does so, the ‘club/hand/wrist unit’ also pushes against the lead arm slowing it down.
The above is a very simplified explanation.