Correct me if I'm wrong, but this is my shpiel of most likely incorrect information....
I'm rather shabby as to knowledge in Linux environment but here's what I've thought of....
For the actual computer of the system, something inexpensive yet highly versatile: the Raspberry Pi.
For the software bit, Raspbian, a Linux-based OS for the RPi could be a valid candidate.
I haven't actually done any Linux exports, but I assume, like the Windows ones, they are a single executable, and with the right softwares, you might be able to launch it. It wouldn't be easy as simply sticking a file on the system and launching it, but it it possible. The Linux system is very flexible.
As for the controller, perhaps there is some sort of third-party adapter for the platform, but I'm not sure.
Just throwing this idea out there, because I've been considering the same thing myself!