Up to a point that text makes a lot of sense for describing a PID controller, which is a form of control that only really looks at error and tries to get it to zero.
As the name implies the PID controller relies on proportional, integral and derivative information about the error. What you mean is a purely P controller, which just relies on the error.
Missiles are also not guided by a PID controller, that would be silly. They (or the guidance computer in the airplane) has to take into account the trajectory of the target and guide the missile in a way to intercept that target, which is not something you can accomplish with just a PID controller.
Modern missiles do better than this, but a missile wired this way with a proximity fuse would hit the target a reasonable amount of the time. Not silly at all if you haven’t invented microcontrollers yet.
From Tactical and Strategic Missile Guidance Sixth Edition.
(To preempt the confusion. Proportional navigation isn't a simple P controller, the missile is seeking an intercept path)
>Not silly at all if you haven’t invented microcontrollers yet.
Apparently the Germans did try that during WW2, but such a missile can not be effective, outside of e.g. bomber intercept.
The "magic" of the AIM-9 Series is that it could achieve this without micro controllers.
>The "magic" of the AIM-9 Series is that it could achieve this without micro controllers.