That's actually not using any of the GPIOs -- although it will require connecting to a 5V and ground pin (all Pi's have a few of both).
The board you see it attached to in the Adafruit ad isn't a Raspberry Pi, or any kind of normal microprocessor dev board (BeagleBone, etc.). It comes with the screen.
It's what is referred to in the description as the "driver board". In this pic, the cable you thought was covering a Pi's GPIO's is connected to the screen itself, and the eight wire adapter on the right goes to the other little PCB with buttons for controlling brightness and contrast, etc.
Notice the HDMI jack on the bottom, which in one of the other pictures (with the actual screen in it), you can see this board in the background with an HDMI cable attached. That's what would be connected to the pi.
So technically, you could use this screen with any device with an HDMI jack and a 5V output. It will not impede your use of the GPIOs in any way, but it does mention it needs 500 mA, which I think is about half of what you could reasonably expect the pi's 5V outputs to supply.