When the quasiparticles travel along one dimension inside the ZrSiS crystals, they do so at the speed of light and are therefore massless. But as soon as they try to travel in a different direction, they hit resistance, slow down and gain mass.
Sounds more like a property of the material than the particle.
Edit: did a little reading. It's not even a real particle, it's a quasi-particle, which apparently means it's a general description of a group of particles.