I've been trying to understand what is meant by words like reduction and reductionism in different contexts. Being somewhat scientifically minded, I enthusiastically embrace reduction as a strategy of explanation when it is done one level at a time. But I get lost when people talk about collapsing all levels down to one, as if that were an end in itself. So here is a loose analogy where things are much simpler. You have the rules of chess (and the objective of winning by checkmate). Most people would agree that there are strategies and principles of play that are objectively good in the sense that they don't depend on anyone's opinion of them. They just tend to work. While nothing is guaranteed, they tend to result in wins and avoid losses.
It's not like a gymnastics competition, where you have to impress judges to score points. If you happen upon a decent chess strategy, you'll tend to beat your opponents even if you don't completely understand why it works. That's assuming they haven't already discovered even better strategies. (I'm using strategy in an expanded sense that also includes the recognition of tactical opportunities, and general rules of thumb like "castle early". What I do not mean by strategy is what game theorists mean by it--i.e. an extensive form/tree that lists the reply to every possible move your opponent could make. EDIT: In other words, I'm referring to heuristics.)
Given the rules and objective of the game, all possible games of chess can, in principle, be enumerated. The rules determine the set all possible future positions, including checkmate positions. In other words, the rules determine all legal move sequences leading to a termination of the game.
Does that mean that good chess strategy can be reduced to the rules?