It does mention it in the paper if you read hard enough, especially the summary.
It looks to me that the anode and cathode is different materials. Yes, Lithium is being plated at each of the anode or cathode during each charge/discharge cycles, but the materials at the cathode and anode are different.are different. Look at figure 4.
The membranes were heated to T 4 130 1C to outgas the ethanol of the applied electrolyte slurry and to reform the solid glass electrolyte without grain boundaries before being pressed against an anode of lithium or sodium foil contacting a stainless-steel cell container. The thickness of the electrolyte membrane was 0.06 mm. The cathode consisted of a redox center (an S8 or ferrocene molecule or an MnO2 particle) embedded in a mix of electrolyte and carbon contacting a copper current collector; the redox center could be removed.