Although I disagree with the notion that pool is somehow correct, perfect, or complete, there are a few properties of pool equipment that may make it seem that way at times because they allow us to easily model an approximation of their behavior. The spherical shape of the balls, flat and level slate surface, right angles of the rails, approximately 2:1 ratio of playing surface length to width, etc. all "simplify" the game enough that we can come up with geometrical models that are close enough to get the job done some of the time. Throw in some knowledge of the physics of motion, friction, and elastic collisions, and you can create models that very accurately describe the way the equipment reacts that are actually useful if you take an analytic approach to the game. While that may seem cool to some students of the game, I think that the true allure of the game lies elsewhere...
What I believe makes pool such a pleasure is that for every shot, the player's interaction with the equipment is limited to the tip of the cue touching the cue ball for a split second to set things into motion. After that, we get to observe the effects of that interaction and wait for the dust to settle before we step back in and give the cue ball another poke. The complexity and precision of motion that we achieve with that brief touch of the cue is, I believe, the primary source of fascination with pool. The feeling of control as the cue ball rolls around doing your bidding and comes to rest in perfect position to perform the next task is unlike anything I've known in any other game.