Back when I was playing competitive Pokemon, I'd remember the top 100 most used pokemon in competitions, their top 5 or 6 builds, the obscure moves that they'd use (Hidden power targets), the common stats that people would build towards (102 speed Jolly Garchomp will outrun a 110 speed Modest Gengar. +50% Dragondanced Jolly Gyarados will outrun a 130 Timid Tapu Koko), as well as OHKO targets of each pokemon (+50% boosted Jolly Gyarados will not OHKO Tapu Koko with Waterfall and is therefore forced to switch).
Because items were hidden information: it was important to memorize these details to know what items your opponent was using. A Gengar will do 30% against my Tank, but some items may increase the damage to say, 45%. If I saw that Gengar did 45% damage with Shadow Ball instead of the expected 30% damage, I knew that Gengar was equipped with Choice-Specs, and that Gengar was now locked-in on Shadow Ball (Choice-Specs gives +50% damage but forces the Pokemon to use the same move-over-and-over, meaning Gengar only has two options: use Shadow Ball again, or switch out. I can therefore better plan around the opponent, despite taking extra damage I wasn't expecting)
I'd also memorize common "cores": Celebi is commonly paired with Heatran back in Gen4 (Diamond / Pearl), because their types perfectly complement each other (especially in Gen4 when Steel was a Dark and Ghost resist). So if you saw that one player has a Celebi, it almost guarantees that they also have a Heatran on their team (Pokemon back then was a game of hidden information: you didn't know what was on the opponent's team until they threw a Pokemon out). Modern Pokemon games reveal the teams these days, so this kind of memorization is no longer needed.
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The overall metagame evolved month-to-month, requiring a new effort to memorize the newest strategies, cores, and builds to keep up with your opponents.
I'm sure there are many other games of partial-information that become memorization heavy. Magic the Gathering is probably another one (which I also played, but never "competitively").
Ex: seeing a few Human cards in Innistrad is an indicator that the player might have a Angel of Glory's Rise in their deck (resurrect all Humans, destroy all Zombies). Figuring out the opponent's "bomb card" before they play it is hugely important.
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Anyone playing a "team-building" or "deck-building" competitive game is almost surely a memorization king. I placed all of this effort into the game mostly because I knew my opponents placed that effort into the game, and that I'd need to push a similar level of effort to "keep up" with them.