You're asking the right questions, but it's laid out in the paper itself, which is linked from the CNN article. I'm going to admit I didn't bother reading the CNN article beyond where the paper itself is linked, but here's what the paper says after showing the equations:
Upon exhaustion following reaction 2, a passage of NaCl solution or seawater at near-neutral pH causes desorption of HCO3− (Eq. 3), leading to an aqueous exit stream with moderately high alkalinity. This unique attribute that CO2 captured from the air is desorbed and simultaneously sequestered as alkalinity in one step into an aqueous stream makes the process distinctively unique compared to other sorption-desorption processes, in which CO2 is recovered as gas and often injected underground for geological storage (7). Note that the salinity or the total dissolved solids of the spent regenerant remain nearly the same, with an increase in alkalinity due to stoichiometric ion exchange. Once in chloride form, the CO2 sorbent can be converted to hydroxyl form, Polyam-N-Cu2+(OH−)2, by the stoichiometric passage of equivalent amounts of dilute OH− as NaOH or Ca(OH)2 (Eq. 4).
