Most modern boardgames do something like that (although typically in a single book with multiple sections).

The standard seems to be to start with a setup/quick start guide that walks you through the initial setup and the in-order game loop.

Then have a reference section that goes through all of the specific mechanics (e.g., a deckbuilder might have "then play a card from your hand" in the quick start, and the reference section would go through the various cards available).

Then at the end is a FAQ, that is mostly just all of the rule lawyer stuff.

Modern games also tend to be better at not needing new players to refer to the rulebook as they used to. Nowadays, you almost always get some form of a cheat sheet card that explains the core game loop, and many rules will be encoded in some way on the game elements themselves.

Now that I think about it, technical writing classes should really take field trips to game stores. There is a lot of impressive that goes into communicating how to play that most people never notice.