Some people just like puzzles.
How legit are the first 3 positions on the leaderboard?
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Welcome to reality! Did you know there is an organization of puzzle lovers - both puzzle solvers and puzzle makers - completely independent of FIDE and with meetings and tournaments on the subject of chess puzzles? The name of that organization is WFCC, World Federation of Chess Composition and many of its members do not care a lot about chess games or chess ratings. Btw, they do not speak of puzzles but of problems and endgame studies.
The object puzzle solvers hate most is the clock. Their mind is set on perfection, not on speed. Some are willing to spend many hours to find a solution and a clock is merely a distraction in that process. That's why they will often score low in timed challenges like the ones you mention. Chess.coms only puzzle service attractive to them is "Puzzle Rush Survival" without time restrictions though its puzzles are relatively uninteresting for real problem lovers!
I was curious what kind of monsters are the people on top so I checked their stats and I really wasn't expecting to find that someone with 96% accuracy over 16000 puzzles would have <80% accuracy games vs. 1100 bots.
Or that person with 90% accuracy who apparently solved tens of thousands of puzzles never made in past 30 in puzzle rush.