This statement seems to want to make the reader think that there is a difference between CO2 emitted by nature and CO2 emitted by humans. It is the same molecule. CO2 = CO2. This process, or any other, can't tell the difference.
Furthermore, there already are natural process that take carbon dioxide out of the atmosphere and turn it into rock.
Carbon dioxide from the air dissolves into the water of the ocean. Animals which create seashells take dissolved carbon dioxide in the ocean and combine it with Calcium, creating calcium carbonate seashells. After the organism dies, the shell sinks to the bottom of the ocean. Sometimes there are enough shells that compressed sedimentary rock, limestone and chalk, are formed. The chalk of the "White Cliffs of Dover" were created this way.
This actually isn't a good thing. Once the limestone is made, nothing in nature puts the carbon dioxide back into the atmosphere. The Earth used to have a lot more carbon dioxide in the atmosphere than it does now, but it has been sequestered into limestone. In about 11 millioin years, the carbon dioxide in the atmosphere will be used up, and life on Earth will be extinguished.
I read it that the plant would take production related CO2 (human industrially produced) and pump it into igneous rock. That might reduce your reasonable objections.