I’ve seen one of these but not working and not close-up, however I’ve not looked up how this works, but as I have a few mechanical calculators, what I think is happening here is:
He enters 22 on the keypad - this is transfered to the bottom row of digits.
He then enters 7 and divide.
At this point the machine is subtracting 7 from the 22 on the bottom and when it rolls over the bottom row of dials shifts one position to the right and back again.
(There is a visible shift right then left of the bottom row of dials)
My suspicion is that this action is moving an index gear inside it (right wards) to select the next digit on the bottom to do the subtract from - which at the same time has moved the subtraction counter (ie. the result) on the top tow of dials.
Missing is the reset and setup actions which I suspect moves that index wheel all the way back to the left. (With, I suspect, a lot of noise!)