I said "physical" because I wanted to include things other than elementary particles but that behave in a way consistent with what I think is a typical non-physicist general intuition about particles: "somewhat long lived (sufficient to be resolved not just by decay products) point-like objects".

Some elementary particles (quarks) don't really obey a lot of this intuition. Some none-elementary particles, for example protons/neutrons, do follow a lot of this intuition. Even some topological order quasiparticle in CMP follow this intuition -- magnetic skyrmions can be localized, can be imaged, have particle-like scattering.

Anyons don't follow this particle intuition.

Yeah, the problem with that is that a lot of quasiparticles do follow that intuition (as do anyons except they exist in a 2D world that isn't normally possible to experiment in).

In particular photons travelling through a medium are usually viewed as quasiparticles travelling slower than the speed of light, rather than a complex system of interactions. These particles have exactly the same kinds of behaviour as normal particles, similar to photons except with mass.

What else would they be?

Emergent phenomena. Like how a row of toppling dominos will have a front which seems to move through the dominos, but is actually just a long chain of mostly stationary dominos. It would be odd to argue the front is a physical object.

Taking this further you might conclude that a soundwave isn't physical either. And sound is actually an examples of quasiparticles (phonons) when you get down to the quantum level.

Then again most people would be of the opinion that light propagates slower through solids like glass, but the photons in that description are quasiparticles (which have mass, unlike the photons in isolation). And quasiparticles share many properties that you'd normally expect only physical particles to have so it gets complicated.

Arbitrary classifications like national borders.