😛R3 is a neutral ligand (assuming R is a neutral alkyl group), and and the 3 Cl- ligands each have a charge of -1. Because the overall coordination compound is neutral, the Rhodium must have a charge of +3 to balance the three -1 charges from Cl-. So the TM here is Rh(III).
This would be a d6 octahedral compound. It's not easy to say whether its HS or LS since the Cl-s are pi donors while the 😛R3s are pi acceptors, and on the opposite end of the spectrochemical series.
This looks really similar to Wilkinson's catalyst - just has two extra chlorine atoms. In Wilkinson's catalyst, the central rhodium atom is bonded to a chlorine (or in this case, 3 chlorines) and then three PPh3 groups. I suspect that the authors of the Berkeley review are using PR3 as a substitute or shorthand for the PPh3 that's used in that catalyst.
Since the PPh3 (or PR3) group isn't charged, then the formal charge of the central rhodium has to be +3, since there are three negatively charged chlorine atoms.
Not at all clear to me when I worked that passage for the first time and even after the fact, it took about 30 minutes of soul-searching to figure it out.