The weight in the Mars Rover Parachute will make it come down if there is no atmosphere. The atmospheric layer is the one which makes matter stay on mars and if it is absent, the body will automatically come down because the weight will not be supported by anything.
Lowheadroom is correct; Mars DOES have an "atmosphere", but nowhere near as thick as the Earth's. That atmosphere is what allows parachutes to work; the Curiosity parachute was far larger than what a similar suitable one would have needed to be in this atmosphere!
Lowheadroom had it right the first time! There is no oxygen on Mars, but plenty of atmosphere - CO2 mainly.. Which is why NASA can use a parachute to slow the craft down to allow a soft landing. And why there are endless dust storms on the Martian surface.