> Chess only teaches two general lessons about strategy: look more than one step ahead, and invent heuristics

That is true for an engine.

Meta-games around studying your opponent, specific match preparation and all those game theoretic stuff are so pervasive people claim they are 'killing' chess at top levels. Anyway, for humans, chess at high levels of mastery is a striking display of bootstrapping some insane cognitive machinery around memory, processing speed, 'expanding' working memory via understanding:

[0] Alekhine blindfold simultaneous vs 32 opponents: https://www.blindfoldchess.net/assets/images/alekhine-excerp...

[1] Reingold, Charness, Pomplun & Stampe (2001), "Visual Span in Expert Chess Players": https://pubmed.ncbi.nlm.nih.gov/11294228/

[2] Connors, Burns & Campitelli (2011), "Expertise in Complex Decision Making: The Role of Search in Chess 70 Years After de Groot": https://onlinelibrary.wiley.com/doi/epdf/10.1111/j.1551-6709...