They inject a few tons of water to trap a ton of CO2.

I'm not sure it has any real value opposed to injection into a saline aquifer or old oil field.

Solving climate change AND sea rising at the same time. Too bad we may end having as much water as Dune by the time we reach a healthy amount of CO2.

They're working on using seawater in their process, which directly addresses that issue, no?

Their wikipedia page says 25 tons of water are required for every ton of carbon dioxide.

First, they'll have to expend energy to pump all that seawater to wherever they want to inject it. Will CO2 be created to generate that energy? What percentage of a CO2-producing power plant's output will be required to move all the water around?

Second, what potential does injecting all that brine have to spoil underground sources of fresh water?

And meanwhile there is nothing known to be wrong with just injecting the CO2 into a saline aquifer, which you can find in most places.