Works over Wi-Fi? Is there a screen on the back and a keypad to type the password and select the network? Wifi takes a lot of power. Does it use AAAs, or do you have to periodically recharge the batteries? That surely would be impractical. Especially if you have a button for multiple products in your house, as shown in the video - maintaining five or six of these things would be a pain. A separate Amazon app or a component of the Amazon app with a list of products you plan on reordering periodically seems much more practical.

Just doesn't seem plausible. April Fools is tomorrow.

The app on your phone uses wifi. I'd expect the buttons use Bluetooth's low-energy variant.

My reading of it is that the app on the phone is used to configure the button, and the button from then on operates independently (which would be good in that it would allows others to use it when the original person isn't around). It's ambiguous, though, and could go either way.

Given that it would literally only have to connect to the wifi and do the API calls when the button is pressed, the power usage would be minuscule.

You could have a button next to the button to order more batteries.