# Pressure: Measurement vs Definition?

I'm a bit confused about the relation between how we measure pressure and how it is defined. Consider a gas inside a container, if we connect a manometer and read the height difference, we say that the "pressure" for example is x mmHg (if mercury is used). Now, we do we say that this "Reading" is equal to the weight of the column of mercury that was raised divided by the cross sectional area?
I get that we can define a quantity called pressure that is equal to the "intensity" of the force over the area, so that P=F/A. And we can say that the weight of the column of mercury would exert a pressure of x Pa over some area. But, my question is, why do we say that this reading means that the gas is exerting a pressure (equal to the pressure that the column of mercury would exert) on the container walls? Such that on each small area A of the walls of the container, there is a force equal to PA? How do we know that? Is there a way of measuring the force on an area A on the walls?