So with the price drop I've been mulling over getting an Nvidia Shield. One piece of info I can't seem to find is if GOG games work with it. I don't know if it's specifically looking for Steam, or if you can load any old DirectX or OpenGL program to it.

Does anyone here have one, if so does it work?

I would say, only games from this list are supported - http://shield.nvidia.com/pc-game-list/

edit: but no idea about Steam only

It's an Android device, so no.

It streams from PC.