Power A MOGA
BDA's Bluetooth Game Controller
My wife worked for Bensussan Deutch & Associates (BDA) back around 2013 or so. During that time, they had started another company called "Power A", a video game peripherals company, based out of Woodinville WA. And their first product was this - the Moga (Pocket). I got one of the first ones made for Christmas 2013 IIRC. BDA has since sold the Power A division to ACCO brands.

The Moga, or Moga Pocket as its now called, is a small, bluetooth game controller you can attach to your Android device to use like a gamepad. It features 2 analog sticks, 4 control buttons, and 2 shoulder buttons, and clips your cell phone neatly into it's top piece. It uses Bluetooth so it could work with other platforms or systems. It comes in a nice leather pouch and runs off 2 AAA batteries with a battery life of about 6 hours.