The wifi and a tiny microcontroller are available for around $5 in single units these days - google "esp8266" - I'm only _marginally_ surprised Amazon can ship these for $5, but I bet they aren't making much (if any) loss on these at their volumes.
If $5 was near their costs, wouldn't they then sell it for 2$ or something, because Amazon (and their brand partner) make money with the button later?
I bet the $5 price point is something they arrived at mostly by asking what customers are _willing_ to pay.
That whole concept is so new they would not hinder it's success by making the button $10 or anything near the true cost. Amazon is all about investing in growth, and this is very likely an investment. Maybe not even that much in additional sales, but in mindshare for a totally new and unique shopping experience.
All of that does not work for an open "does anything you want"-button, so anybody designing and selling such a thing would have to think very very different about the hardware cost.
My suspicion is perhaps someone said "Make them free! We'll make _heaps_ more out of the sales than they cost!", and someone else (probably a greybeard with enough experience to remember) said "Hey, remember CueCat? Maybe we need to 'sell' them for at least enough that when someone works out a good use for them that _doesn't_ result in retail sales, we won't be too unhappy with people flocking to grab them from us..."
