The answer is that the molecules in the atmosphere do fall to the ground, but when they get there they just bounce right back up.
You might say that begs the question, because when you drop a ball or other large object, it bounces lower each time and eventually comes to rest. What's the difference, then, between the ball and the molecules in the atmosphere? Why don't they eventually come to rest?
From the discussion on the previous page it should be clear that the answer to this question is that the ball has zillions of microscopic "jiggling" degrees of freedom, whereas the molecules do not (they actually do have one or two, often, but never as many as a ball, which has a million billion billion). When you drop the ball, the energy of the bouncing degree of freedom quickly flows into the jiggling degrees of freedom. Since there are so many of these, what remains in the bouncing degree of freedom after the initial energy has been parceled out equally is very, very little energy. In the case of the atmosphere there are no (or hardly any) jiggling motions, so the bouncing energy of the molecules simply has nowhere to go.
You can verify the difference between a macroscopic ball and the atmosphere yourself with the simulation --- just compare dropping the box with springs intact to dropping the separate atoms with the spring strength set to zero. You will see in the first case the typical behaviour of a macroscopic object, namely heating up and coming to rest, and in the second case the behaviour of separate atoms, namely bouncing up forever to the same height.
Incidentally, if you want to experiment more with simulations of the atmosphere, check out The Ideal Atmosphere simulation.