Carboxylic Acid to Acyl Chloride
They should both work. I would use oxalyl chloride with a solvent like DCM. DMF should act as a catalyst here for the acid chloride formation. (I don't have access to the paper but this is most likely what they have done) The oxalyl chloride reaction is maybe easier to work-up although I don't think there is a big difference when working in lab scale. In this case you can skip work-up (assuming you have used DCM as solvent and 1-2 equivalents of oxalyl chloride) and just add $\ce{AlCl3}$ for the cyclisation step.

EDIT: You can read the experimental in the supporting info -page S7