That process absorbs CO2 from the atmosphere at low concentrations (400 ppm) onto stones coated with X-material. Later the stones are heated (using more fuel) to release CO2 at much higher concentrations (more than 75%). Then what? It is a gas. You need to bury the carbon. They suggest feeding it to greenhouses, to grow food, which re-releases it later.
See http://www.climatecentral.org/news/first-commercial-co2-capt... .