This would be a good demoscene category. Sadly it looks like pouet.net doesn't have a "platform" category for raw x86 (I think some of the DOS entries will be this, but not all) and I only saw one entry for x86.

At the end of the day: I think MS-DOS is a more attractive target than raw x86. It does a few things for you, but then mostly gets out of the way if you don't want to use its features, and has better accessibility (thanks to DOSBOX) for most users.

Would a game that is essentially a micro Linux distro count? I feel that should be pretty doable as a bootable USB stick or CD.

If you did it that way you'd have to bundle the Linux kernel plus graphics drivers at a minimum. But I wonder how much of the OS you could avoid having. Certainly you wouldn't need a Desktop Environment. I wonder if you would need something like X or Wayland or if you could get away without that (to run games built in a normal-ish userspace way). I guess finding the minimal environment for SDL would be a good starting point. That sounds like an interesting exercise for sure.

Although something like that probably isn't as pure as you're looking for, it would be pretty cool to do anyway. Maybe we should start a club.