From the record
“The Amistad Gymnasium is a historic gymnasium located in Amistad, New Mexico. The gymnasium was proposed in 1935 by the Works Progress Administration; construction was completed in 1937.”
Wikipedia article Amistad Gymnasium, CC BY-SA 4.0.
One of 11 National Register listings published here for Union County · listed in 1996 · category: Building · built in 1937, Art Deco architecture, by Works Progress Administration.
Sources: the Wikipedia article · the case file at the National Archives · the National Register database, National Park Service