I don’t know about UChicago, but I’m familiar with Caltech. Caltech students have always had the highest SAT scores by a significant margin for as long as I can remember (i.e. decades), long before USNews started to rank colleges. It has the highest scores for two reasons:
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The school has the most self-selected group of applicants among all colleges. The majority, and perhaps most, of its applicants have near-perfect test scores or better; and
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Because of the nearly unmatched rigor of its program and its small size (fewer than 1k undergrads), the school places greater emphasis on its students’ ability to successfully finish its program. It does this by scrutinizing its applicants for their academic prowess more than its peers (often with the involvement of its faculty).
The higher test scores are just the result of its process, not the other around. As @ucbalumnus mentioned, it’s doing away with the test scores completely (becoming test-blind) for the next two application seasons. It may be in a unique position to be able to pull that off.