I would consider land around a national monument a "park".
There are 128 protected areas in the United States known as national monuments. The President of the United States can establish a national monument by presidential proclamation, while the United States Congress can do so by legislation. The president's authority arises from the Antiquities Act of 1906, which authorizes the president to proclaim "historic landmarks, historic and prehistoric structures, and other objects of historic or scientific interest" as national monuments.
The link you posted shows at least eight different Federal agencies with jurisdiction over various monuments. And some of them have no police capabilities at all.