The PD archives show both the North Kingshighway Sears and the South Grand Sears stores completed and opening a few days apart in September of 1928, so it can't be the main buildings. Maybe out buildings, like an auto center? Did they even have those in 1940?
Just now checked the archives for 1940, and the 9/29/1940 edition shows Sears did open an auto center at the South Grand Store, with it fronting on Arkansas Avenue.
The article also stated Sears had just started work on a warehouse at 1008 South Vandeventer Avenue.