This isn't really a method for extracting CO2 from the air so much as a method to make sure that plant matter which has already extracted it from the air doesn't return it via burning or decomposition. It makes plants carbon negative instead of carbon neutral.
I don't really see the point of burying it when turning it into building materials would be much more effective, by replacing carbon-generating building materials (and being a great insulator). It might be a bit more expensive but building materials have value so it would be more cost-effective? Wood chip is already used to insulate buildings. I don't get why they just want to bury this stuff instead of making good use of it.