This paper proposes that baryons are holographically equivalent to anyons on a 2-sphere. I see basically two propositions here. One is that there is a duality between the description of quarks as fermions with fractional electric charge, and another description in which they are anyons with integer charge. The other is that confinement is the manifestation in the bulk, of a kind of exclusion principle for the boundary anyons whereby they can only be added or removed in groups of integer charge.
There is no model presented, the words "QCD" and "color" appear nowhere in the paper, nor is there any discussion of mesons, gluons, deconfinement... The genesis of the paper is probably just with the thought that the fractional charges of quarks are like the fractionalized charges of quantum Hall anyons - I had that thought too (and so surely did many people), I just never combined it with holography.
One might be tempted to dismiss the paper as a superficial speculation. However, a few things give me pause. There is a history of speculation about integer charges for quarks, starting with the Han-Nambu charge assignment (which does not match experiment). If one studies anomaly cancellation in the standard model plus gravity, there are two hypercharge assignments which work: one is the standard model as we know it, the other is a so-called "bizarre" assignment in which the quarks have integer hypercharge. S.A. Abbas has recently claimed that the bizarre hypercharges actually correspond to a valid dual description of nuclear physics.
Meanwhile, there is now a body of work in mainstream AdS/CFT, studying bulk duals of anyonic systems, in which the anyons are obtained by a kind of electric-magnetic duality transformation on a conventional CFT. And just today (!), Gorsky et al have suggested that such a transformation maps to a new isotopic/baryonic duality of QCD.
So for me the bottom line is that, although this is a "what if" paper that doesn't engage much with the actual details of either hadronic physics or holography, the bare idea that baryons may, under certain circumstances, have an anyonic dual, is not easily refuted. The final verdict on that hypothesis awaits the outcome of these more sophisticated and rigorous investigations.
Update, December 2018: Zohar Komargodski today released a paper, Baryons as Quantum Hall Droplets, in which single-flavor baryons made of light quarks (i.e. uuu and ddd) are described as membranes of η′-meson condensate, in which deconfined anyonic quarks are embedded. The quarks become anyonic because they are embedded in a two-dimensional surface.