Limited" is a misnomer anyway. Both "limited" and "full" have the same 8-bit, 256 step range. If anything, "full" actually has less dynamic range, since in order to maintain the same black and white points as limited/normal, it has to rip out and expand the 16-235 range to 0-255, causing banding. In case that's confusing:
Limited = 256 steps, 0-16 is considered below black, and should be clipped. 235-255 is considered above white, but is usually displayed. It's called 16-235 because that's the "valid" range, NOT because it actually has less steps. Effective dynamic range = 240 steps. If a game actually has below black (0-16) info, and you choose not to clip below 16, you'll have the full 256 steps.
Full = 256 steps, but they're created by ripping the 16-235 range out of the "normal" limited signal and artificially expanding. Since we're dealing with integer values, some steps need to be repeated, which causes banding. Effective dynamic range = 220 steps.
Unless a game itself recognizes it's in 0-255 mode and renders the full 255 steps,
limited is technically superior. But since you can change the setting in the middle of gameplay without having to restart the game, I highly doubt that's happening. Far more likely the game has no idea, and the OS is just doing the conversion the crude way.