GNU C Library
An operating system based on the Linux kernel and customized specifically for gaming, could adopt the vanilla Linux kernel with only little changes, or—like the Android operating system—be based on a relative extensively modified Linux kernel. It could adopt GNU C Library or Bionic or something like it. The entire middleware or parts of it, could very well be closed-source and proprietary software; the same is true for the video games. There are free and open-source video games available for the Linux operating system, as well as proprietary ones.