If your going to abstract them that far then you can keep going until almost all games are about pushing a button and seeing a reaction. Not a very useful abstraction. Even if it's only imagined, stealth games put the player into the role of being stealthy and this means their perception and enjoyment of a stealth segment of a game is vastly different to they way they feel avoiding a stomper on a scroller. That difference is extremely important and your comment suggests it isn't.
Which is pretty much what I said when I first read Raph's book. And Raph said this:
I don't intend to come across like the dressing is unimportant, or only relevant to mass market games. Chapter 10 is all about how experience design matters, for example. I even use almost your chess example, only with go instead. I also say "The dressing is tremendously important. It's very likely that chess would not have its long-term appeal if the pieces all represented different kinds of snot." ;)
In the book I make the distinction between the person in charge of the formal abstract parts of games (what I called the "ludemographer") and the person in charge of the game experience (call them the director, if you like).
The avenues of enjoyment beyond ludemography that the director taps into are well understood. They are story, they are art direction, they are music, etc. The thrill from getting the headshot, the tactile feel of real go beads on a wooden board. And even though they are well-understood, they aren't EASY--so I think it's perfectly valid for you to spend a lot of time thinking about those things.
I argue that the fun brought by pure ludemography is the core of gameplay and the part that is not as well understood as it should be, and that's what the bulk of the book is about.
Which is why this "Game Mechanic Map" might point out that a "stealth game" with guards and patrolling is just over the hill from a platformer with stompers in the same way that meringue is just over the hill from an omelet. This "Game Mechanic Map" would be just for the salad AKA style AKA mechanics and we'll leave the dressing AKA substance AKA color for other books.
Actually, I believe color is more important than the mechanics. The reason I'm addicted to Guitar Hero is because the color taps into a core fantasy; yes, the formal rules are slightly different and possibly improved from Amplitude & Frequency but that's not what gets my glands pumping. (And imagine if these games played random tones instead of music when you got the notes right.)
Still, like Raph, I think it's useful to strip away color when discussing mechanics if we're going to figure out why one mechanic "works" better than another.