In areas like political or social debates, a disputant is the person who takes part in a dispute. In words put simply, a disputant is a debater. He/she states her arguments on significant world problems or issues based on his/her experience, research and moral principles. When there is a conflict resolution, it means that there is an agreement reached by the two disputants or debaters.
I believe this is a metaphor, as it refers to one thing in order to show or suggest they are similar. The phrase means that, as how a desert can survive winds and remain steady, so is their love for each-other. No matter what happens, Fatima and Santiago’s love will forever be true-hearted and faithful. Hope this helps!