What makes a contest a rivalry game? I think we all know the main parts, anything else?
Proximity (Usually, ND-USC aside).
History/tradition
Competitiveness (No side really dominates).
You could add national significance, but I don't think that is always required but it helps. Alabama-Auburn is often considered the 2nd or 3rd "best" rivalry game even though one team has dominated, usually, and the other has a somewhat mediocre history.
USCe-Clemson is big in that state.