Actually, several games have their own spin on Mars, though liberal borrowing of Barsoom seems common.
When the Navy Walked has a Mars supplement that has green, red, and white Martians. Bob Charrette's Valor, Steel, and Flesh seems similarly influenced.
Terry Sofian's Hive, Queen, and Country has a bit different spin, though I've not delved deeply into the Martian world as he sees it.
I had a print-yourself RPG simply called MARS, which felt more fantasy, but I think it had VSF elements. Been awhile since I looked at it.
Several others popped into mind, and as quickly out, a common occurrence when recalling too much in too short a time. I'll add as I recall.
Doug