Of course it does. It has the power to purchase property. In fact, it has the power to seize property, as long as the owner is compensated appropriately for the loss. What country do you live in again?
States don't have "rights." They have powers which are allocated to them by the Constitution.
Individual rights are not abridged by public ownership of land or property. Your freedom was not curtailed because Yellowstone wasn't turned into a quarry and condos.
Central Park is a critical component of New York City. It's a vital resource, which provides the community with space to assemble, to recreate, to relax and to exercise. It's an international tourist destination, and its existence enhances property values all the way around the park. No private individual can provide the same functionality -- because if that land was privately owned, the owner could discontinue public access at any time, for any reason.
What about Acadia National Park? A bunch of citizens purchased land, and intentionally donated it to the federal government on the condition that it would become a national park. Why don't those property owners have the right to dispose of their land in this way?
To me, this anti-park line of argument illustrates one of the problems with libertarianism: It refuses to acknowledge the benefit of common goods.