From the record
“The Dakota Club Library in Eagle Butte, South Dakota, also known as the Eagle Butte Library, was built in 1910. It was listed on the National Register of Historic Places in 2004.”
Wikipedia article Dakota Club Library, CC BY-SA 4.0.
One of 5 National Register listings published here for Dewey County · listed in 2004 · category: Building · built in 1910.
Sources: the Wikipedia article · the case file at the National Archives · the National Register database, National Park Service