I don't think it means that the federal governent can take over land belonging to a state either. But it does not preclude the government owning land and other proptery within the borders of a state.
Well I have a problem with that. Did the government purchase that land? Was that purchase approved first by the state and then by the peoples representatives?
DoodleDawg - Article 1 section 8 is the relevant section here and yes, the government can own the land. Also relevant is how the government obtained the land as Nevada was not even a state at the time.
The land came to the use as a result of the end of the US Mexico war in the treaty of Guadalupe Hidalgo where Mexico ceded the land to the US Government. That means the treaty clause under Article II section 2 comes into play as well.