It doesn't explain the rotation curves of galaxies at all, and doesn't try to. It takes a simple proxy for an isolated galaxy and sees if there are physically

It doesn't explain the rotation curves of galaxies at all, and doesn't try to. It takes a simple proxy for an isolated galaxy and sees if there are physically reasonable orbits around it. MOND-like orbits are physically reasonable (we observe them). The authors' model allows for almost MOND-like orbits. The explanation for why these MOND-like orbits exist will vary. In the standard cosmology, it's because of a distribution of cold dark matter around the central mass. In MOND, it's because the strength of Newtonian gravitation falls off at great range from the central mass. In the theory discussed above it's because the central mass induces fluctuations in the gravitational field that grow in relevance with distance from the central mass, and in a particular range of radial distances those fluctuations are most likely to drop the orbiting body onto a closer orbit.