I do not understand how, by this model of atmospheric pressure, the reason of atmospheric pressure can be explained in a closed room say.
Let's take your closed room to it's most extreme, a sealed tank containing a gas in deep space. There's no need to worry about gravity, or the fact that the Earth's atmosphere is exposed to vacuum. The pressure of the gas in the tank is a function of density, makeup, and temperature of the gas.
Ideally, the relation between pressure, density, makeup, and temperature is a very simple function, $P=\rho R^\ast T$, where $P$ is the pressure of the gas, $\rho$ is the density of the gas, $R^\ast$ is a constant that is specific to the makeup of the gas, and $T$ is the absolute temperature of the gas. Alternatively, $PV=nRT$, where $n$ is the number of particles and $R$ is the universal gas constant. Both $P=\rho R^\ast T$ and $PV=nRT$ are expressions of the ideal gas law. You need to understand the ideal gas law and its ramifications to have any understanding of the behavior of real gases.
The behavior of the gas in that sealed tank is not quite so simple in a domain where gravitation is non-negligible. The pressure in that idealized sealed tank of gas is no longer uniform when that gas tank is at rest on the surface of the Earth and the gas is in an equilibrium state. A careful experimenter will find that the pressure varies with height. This is because the gas is in a state of hydrostatic equilibrium.