It seems what they do is Ocean Water + Sorbent -> Leaches Carbonates for use in Cement -> Heated in Kiln -> Releases C02 -> Captured and redissolved in Ocean water. This still has to be proved how to reabsorb such large amounts of c02 in ocean water.
Absorbing large amounts of CO2 happens every second since 2-3 centuries at this point, and is the main driver of ocean acidification and subsequent coral bleaching, loss of wildlife, etc. If the mentioned process could "recycle" the CO2 needed for lime production, then it could be a big win for a very hard to decarbonize sector.
What is still to be checked is how more expensive this lime will be, and how it will stack up compared with traditional limestone+carbon tax
