Linear Regulation Concept Confusion
His explanation is "correct enough" but less clear than it could be.

Your explanation is also "correct enough", but the use of the transfer function curves add more complexity than is needed for a basic explanation.

A basic statement, which is reflected in the transfer function curves is
"A PMOS transistor will exhibit decreasing drain-source resistance as the gate is driven more negative relative to the source".
The opposite also applies - making the gate less negative relative to the source increases Rds.

With the above basic concept to work with, the regulator operates by 


increasing Rds if Vout is too high,   
and reducing Rds if Vout is too low.   
Rds and Rload form a voltage divider that cause the above action  to drive Vout in the correct direction.


In the circuit in question the opamp / comparator is arranged so that if Vout is > Vref then Vgate is driven higher so |Vgs| decreases so Rds increases so Vout decreases.

Is that easier to understand?
[Explanations that seem simple to one person may not appear simple to another].