Article IV, Section 3: "The Congress shall have power to dispose of and make all needful rules and regulations respecting the territory or other property belonging to the United States; and nothing in this Constitution shall be so construed as to prejudice any claims of the United States, or of any particular state."
That establishes that the federal government can own land and other properties. The land became the property of the U.S. when it was taken from Mexico. Nothing required that ownership be transferred to Nevada when it became a state.
And, in fact, Nevada disclaimed those lands when it became a state. See my post up thread.