A 1940 New Deal Works Projects Administration (WPA) project constructed two peristyles and obelisk monuments in the park (on the north and south sides of Main Street which bisects the plaza).
This is the obelisk on the north side, as the one on the south side was replaced with the statue of George Dealey seen in the previous photo.
The building in the distance is the Texas Schoolbook Depository, which now houses the JFK Museum.