What causes the pressure exerted by gas molecules on their container?
You've answered your own question.
The gas molecules exert this pressure on their container. So, clearly, the cause is the gas particles themselves. Pressure in
#vecP = vecF/A#,
which is the force
Only with gas particles in a closed container can said gas particles exert a force upon a given surface area to give the container any pressure at all. Otherwise, if the container is open or is too large, they're mainly just floating, and the pressure would not be as present as if the container was closed.