I feel like this doesn't qualify as an ordering relationship, because of the circular nature of the wheel: for any two elements a and b (a ≠ b) on the wheel it's both true that a is further clockwise than b and b is further clockwise than a (just keep rotating). This violates the antisymmetry property that an ordering relation should have.

You can fix it by establishing some point on the wheel as "least clockwise" (essentially unfolding it into just a straight line) but that immediately establishes a total ordering.