I think I can understand why the author complains about drilling for math contests. I think it’s the same reason high level chess players complain about opening book. Drilling is not fun and it reduces the creative element of solving the actual problems.

The fact that he wasn’t doing it for fun but for college admissions plays a lot into it as well. That kinda pressure can really kill the fun.

OP says in the article that he didn't understand what he was doing, but was just trying to imitate people who did to try to appear brilliant. And he claimed that most students in club were like this, due to parenting and teaching that was focused on resume building for ignorant Admissions Offices, instead of focused on learning.

It really isn’t. The essay makes this point as well. The acquaintance of his who was most interested in math dropped out of the contest team. He went on to become a mathematician because he was actually interested in understanding higher math and how things fit together.

Drilling is just practicing computational tricks to be able to execute them by heart. This would be true regardless of the amount of time pressure or lack thereof. I’ve taken many math courses that had exams in this style and I always hated them. I much prefer trying to figure out a proof I’d never seen before. For any real work, those computations would be done by a computer anyway.

LeBron James much prefers to slam dunks, but he still has to practice the game ad condition.