Let's just acknowledge that anything big enough to be round is a planet. That's the bare minimum criteria.
Orbit shapes and clear paths don't matter, the Solar system isn't a typical stellar system, many aren't so stable and ordered, especially in binary and triplet star systems. So the pedantry around the shapes of the orbits of the outer kuiper planets is a very silly thing to argue about. After all most orbits in binary and triplet systems aren't even predictable long term, let alone not circular.
I believe the rule of thumb is binary planets' barycentre is external to either body. This is the case with Pluto/Charon, I think it's also the case with Earth/Moon.
Other way around, the further apart the objects are the less likely the barycentre is to be inside one of them, you can picture it as a rubber band with a dot drawn on it, the more you stretch it the further the dot gets from both ends even if it gets further from one end faster.