The way in which I think about it is that "learning" (in humans) often occurs is in the form of heuristics - certain rules or shortcuts which are not guaranteed to be optimal, but do a good job at simplifying (the search-state of) the problem. Instead of trying many simple comparisons between legal moves, we instead use a heuristic to score them.
Non-NN chess engines are really all about doing a good job at balancing these heuristics (like it says above). There's fundamentally an upper bound in how good the overall approach can be, simply because the underlying heuristics are defined and selected by humans: there could be many more heuristics that haven't been considered. This version of "learning" is really just removing human forced constraints which were introduced to help learning, by starting from a position without bias.
Non-NN chess engines are really all about doing a good job at balancing these heuristics (like it says above). There's fundamentally an upper bound in how good the overall approach can be, simply because the underlying heuristics are defined and selected by humans: there could be many more heuristics that haven't been considered. This version of "learning" is really just removing human forced constraints which were introduced to help learning, by starting from a position without bias.