No proper calibration, but the closest I've seen is in the Myst series. According to my fuzzy memory, either Riven or Exile (or both) had a setup screen with shades of gray, it instructed you to adjust the brightness / contrast of your monitor until the shades looked a certain way. My search-fu is failing me on this, so maybe it's a fabricated memory.

A significant fraction of games I've played on Xbox in the last decade have had a setup like that.