Josh Waitzkin also learned in a similar way, and attributed some of his strengths to that. From his book:
Once he had won my confidence, Bruce began our study with a barren chessboard. We took on positions of reduced complexity and clear principles. Our first focus was king and pawn against king— just three pieces on the table. Over time, I gained an excellent intuitive feel for the power of the king and the subtlety of the pawn. I learned the principle of opposition, the hidden potency of empty space, the idea of zugzwang (putting your opponent in a position where any move he makes will destroy his position). Layer by layer we built up my knowledge and my understanding of how to transform axioms into fuel for creative insight. Then we turned to rook endings, bishop endings, knight endings, spending hundreds of hours as I turned seven and eight years old, exploring the operating principles behind positions that I might never see again. This method of study gave me a feeling for the beautiful subtleties of each chess piece, because in relatively clear-cut positions I could focus on what was essential. [...]
Once I experienced these principles, I could apply them to complex positions because they were in my mental framework. However, if you study complicated chess openings and middlegames right off the bat, it is difficult to think in an abstract axiomatic language because all your energies are preoccupied with not blundering. It would be absurd to try to teach a new figure skater the principle of relaxation on the ice by launching straight into triple axels. She should begin with the fundamentals of gliding along the ice, turning, and skating backwards with deepening relaxation. Then, step by step, more and more complicated maneuvers can be absorbed, while she maintains the sense of ease that was initially experienced within the simplest skill set.
Josh Waitzkin also learned in a similar way, and attributed some of his strengths to that. From his book:
More links: deliberate practice, granuralization.