VoCore2 is a one square inch-size computer with support for USB, Ethernet and video. It has a 580 MHz CPU, 128MB of RAM and built-in Wifi, yet remains smaller than just about anything you might use it as a brain for.
On the video below, you can see it running DOOM at the margins of playability with the VoCore2 Screen, one of several official add-ons.
Makes a great router, apparently! I imagine that the systems-on-a-chip inside WiFi SD cards are slightly smaller than this, but you sure as hell ain’t running DOOM on one of those.