The way you used the rivalry was (no offense) lazy, so rounded it down to being no rivalry. You can't place a killable enemy into game and call it rivalry, there's more unique ways to pull it off.
most of the games in this jam used that implementation of rivalry. i chose a gladiator theme because i think it's a good representation of rivalry, and i tried to give the player a grudge against the soldiers through my story, as short as it might have been