The Patch-A-Tron uses the RA8875 video controller board from Adafruit. This controller works via SPI and handles all of the low-level rendering as well as the touchscreen control. This makes it really nice for Arduino. Connection is via the 6 pin SPI connector in the middle of the Mega. (+Vin, GND, MISO, MOSI SCK, RST) with pin 11 on the Arduino being used for the INT and pin 12 for the CS on the RA8875.

In the photo above the blue and green wires go to pin 11, and 12 on the Arduino the rest connect to the 6 pin SPI connector in the center of the Mega. Both the video out and touchscreen in are SPI, so wiring it is extremely simple. (Note also that there is a layer of Kaptan tape and another layer of 2 sided tape insulating and affixing the RA8875 to the aluminum plate. Which is not really visible in the photo. Without it the RA8875 would short out on the faceplate.)

The Patch-A-Tron Arduino Sketch uses the RA8875 library available here -

https://github.com/adafruit/Adafruit_RA8875.