I don't think this paper reveals anything new. It is well known in Newtonian physics that a disc-shaped mass distribution can yield a flat(tish) rotation curve and galaxies are perfectly well-described by Newtonian physics (see Sten's answer). Crucially, that flatness only persists whilst a significant fraction of the mass is still exterior to the test particle. In other words, for a disk with an exponentially decaying density with radius, the rotation curve is indeed flat for in the region of 1-2 exponential scale lengths. Once beyond that, then the rotation curve falls in a pseudo-Keplerian way as expected.
The difficulty is that the density of visible matter in spiral galaxies like the Milky Way has an exponential radial decay length of 2-3 kpc, whilst the rotation curve is flat for >30 kpc.
Thus to explain the rotation curve with a disk, you need the disk to have a density that decays with an exponential scale lengths of 15 kpc or more - at least 5 times that of the visible matter density.
What this means is that once beyond a few kpc, the disk density would need to be dominated by non-luminous mass, a.k.a "dark matter". Thus, no problem has been solved at all.
Worse, because we know what the mass density is in the disk from studying the motion of stars perpendicular to the disk, we know that the mass density in the visible disk is not dominated by dark matter, but by the visible stars and gas.