You could even do away with a full skeletal system in the upper section. Could be almost all muscle around some bones for support and mobility.

Having more ribs isn't a problem for a mammal, those are pretty variable between species, unlike vertebrae. And thats quite a puzzle, how many go into the horse bit, and how many in the human bit? Obviously the horses "neck" and the humans lower back overlap, but it'll still be a puzzle. You'd end up with a less flexible body.

Now, I would think that with the extra space, there would be something like a stomach in there to begin breaking things down before sending them along but that isn't mandatory for the basics to work.

Why? Centaurs aren't ruminants, imagine eating grass with those poor underdeveloped human omnivore teeth, or stripping leafs with human lips, ouch. In fact, feeding a human brain and a horse body with a human mouth is going to be a LOT of work.

If you're going to do tentacle-arms without bones, the human part would basically need to be all muscle, with some weirdly deformed vertebra for shoulders.

And that leads me to another thing. It must have some very intricate blood-pumping systems, because centaur hands can't reach the ground unless they bend aaaaall the way down, like head to knees low. In order to actually use those hands, they'd have to be upside down for long periods, but also right side up for long periods. With a very thirsty human-stylr brain.