Nature Play is in SA, WA and Qld
It is Gov't sponsored in each state but at differing levels.
SA passes may attract funding back to the Parks depending on useage but the level of Gov't sponsorship is unclear.
Yeah, I reckon you are correct "...at any of South Australia’s great Parks listed below with this free vehicle entry pass!" (my underlining)
I reckon thats fair enough to pay for camping for overnighters etc and getting kids out in the bush for a day for the sake of $10 or whatever is a good thing.