White Sands National Park Establishment Act This bill establishes the White Sands National Park in New Mexico as a unit of the National Park System in order to protect, preserve, and restore the park's resources and recreational values and to enhance visitor experiences. The bill abolishes the White Sands National Monument and incorporates the lands and interests that comprise the monument in and as a part of the park. The Department of the Interior shall not nominate the park for inclusion on the World Heritage List of the United Nations Educational, Scientific and Cultural Organization (UNESCO) unless each county in which the park is located concurs in the nomination. Before submitting such a nomination, Interior must notify the Department of the Army of its intention to nominate the park for inclusion on the list. Interior must complete an official boundary survey of the park. The bill modifies the boundaries of the White Sands Missile Range in New Mexico and the Public Land Order 833 (relating to the withdrawal of certain public lands in New Mexico for use by the Army for military purposes and the revoking of certain executive orders and public land orders) to exclude the land transferred to Interior and to include the land transferred to the Army. The Army shall administer the land transferred to it as a part of the missile range.