Sears could have been Amazon. They had the warehouses and distribution system. But not the vision.
Story does get one detail wrong. KMart bought Sears, and then adopted the name. Lampert bought the stores as a real estate play, but kept the operations going longer than people thought he would.
You are right, SEARS was the original Amazon. At least 2/3 of my school clothes were bought annually out of the SEARS catalog. JC Penny, SEARS and one other store I cannot recall the name were big in catalog sales. I have two rifles that say JC Penny on them. One is actually made by Savage, I believe the other was made by Marlin.