It spins with the earth. It would be difficult to talk about the atmosphere in isolation from its interaction with the surface, since many of the atmosphere's properties are linked to the surface below. Flows occur among elements within the system, but there are also external exchanges, as well.
Open systems are very common in the physical environment.
Closed systems are very rare in nature. Hard to isolate a system from all external influence. Expect for occasional meteors coming in and some hydrogen atoms escaping, the earth's substance is finite. Things like water or nitrogen are not exchanged with outer space. We must make do with what we have.