Why isn't a human required to confirm visually that flight controls are moving?
Same linked video @ 7:03


  
    [A] safety measure to forestall the possibility that the [display] shows a flight control to move when it doesn't.
  


The display (above) doesn't mimic the input, it shows the positions of the sensors independent of the input signal. Since the position change that is being checked is confirmed to be related to direct input, the data is valid.

In other words, an unexpected result with/without input would be an issue with a sensor and/or surface.

In lieu of digital displays, planes like the earlier 747 variants and Concorde had analog instruments that also read sensors. And with the hydraulics operating on a plane like the 737, the fact that the controls are able to move the full range unjammed, indicates that the control surfaces are responding and are also unjammed.

It gets trickier with a plane like the MD-80 where the controls move tabs instead of surfaces (a tab is a control surface on a control surface). It has resulted in an overrun in 2017. No human [visual] inspection could have detected it as the tab would have still moved as expected, but not the stuck surface, also as expected – tabs need airflow to move the surface.