Even if it's Wifi, an ESP8266 only uses 78µA in deep sleep mode, which is how these buttons will spend 99.99% of the time, so it could last more an year on a single AA battery.
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.