The page for the Tournament Arc trope seems to (sort of) cover your example in one of it's paragraphs:
...Tournaments are almost always single-elimination; the hero will not face the same opponent more than once. Proper seeding will be entirely ignored, and yet even so the hero will always find himself facing tougher and tougher opponents every round. His final opponent will probably be The Rival or a Big Bad or Dragon.
The 'Tournament Arc' trope itself is fairly broad however your example could be considered a specific subset of it.