Some particles are actual particles - like photons, electrons, protons, etc. Think of them as a droplet of water.

Some particles are not really particles, but kind of behave like a particle in some ways. Think of them as bubbles inside a liquid.

If you ignore the air inside, the bubbles don't really exist - they are just the absence of some liquid, that happens to look sort of like a particle with funky properties. Similarly, the particles described in this article don't really exist - they are "holes" in a lattice of other particles, that can mathematically be treated as if they were particles, but aren't actually real in a non-mathematical way.

That said, if Quantum Mechanics has taught us anything, it's that those "purely mathematical" concepts can have very real impacts on the world, so in a sense, it is exciting that these "pseudo-particles" have been found to exist, because the maths might reveal all sorts of funky shit we can do with them that would be impossible with regular particles, and the maths doesn't care that they're not regular particles - it works with either kind of particle.