Right, below is what it says in the book regarding the final part of the championship:
The next morning, the remaining contestants gather for the final stage of the Topaz Championship. It is a single-elimination iaijutsu dueling competition, fought with blunted steel swords.
After each round, half the contestants are eliminated, until only one remains: the Topaz Champion. Note that all of the contestants who are allowed to enter the tournament must have attained enough points to complete their gempuku—the duels are only to determine who gains the honor of becoming the new Topaz Champion.
There is also a parallel competition for shugenja, known as taryu-jiai. If the winner of this magic-oriented competition has amassed more total points than the winner of the iaijutsu dueling competition, then the shugenja is named Topaz Champion—a very rare occasion to be sure, but one that has happened in the past.
I've added emphasis to highlight what i see as the most pertinent points here so whilst the points do matter it essentially comes down to whoever has the most points out of the winner of the two duelling contests for who get's named Topaz Champion