It doesn't need to be on all the time. It can just take however long it wants to start up, connect, and transmit the order.

i think many people are missing this key point. this isn't a "i need this right this very millisecond" its more of a "i need this later today if its early enough or tomorrow would be fine" button. which a single press of a button would wake up the device, connect to what ever configured network connection it is assigned to, send some data to an API end point, go back to sleep. that could make the button last many years.

"only" 78 microamps is a LOT of current for ultra low power applications like this.

On top of that, ~~the ESP8266 doesn't seem to implement wifi, it's just 2.4ghz general purpose radio.~~

There is definitely some cleverness happening here that allows them to get this to where it is. I'd love to get one just to tear it down.

No, the ESP8266 does implement Wifi. And not only that, as it can also run custom code, so it could be the only IC in the package.

Oh wow! I didn't realize that! Awesome!