But, much like Kris Kringle recommending Woolworths to Macy's customers in "Miracle on 34th Street", getting you the item you want elsewhere doesn't lose Sears a customer - It makes certain they'll check Sears first in the future.
They're sending customers to Amazon's affiliates because it gets them SEO results and they likely get a kickback.
Coming from my searches that've turned up the affiliate spam, these are generally items that have nothing to do with Sears's main product lines or that Sears is well sold out of.