From the video, it appears that they are dipping by 1cm, measuring volume, dipping by 1cm more, measuring volume, etc. So they end up, effectively, with a set of 1cm slices and the volume of each slice. For one orientation. Then they repeat, getting slices at a different orientation.
Not only would it not work with something absorbent, but (per other comments below) does not (currently) work with shapes that trap air or catch liquid.
I think they're 3D-printing test shapes because it's the simplest way to generate interesting test structures. Otherwise they'd have to manufacture (for example) a bunch of columns plus a ball using metalwork or wood or something. Some of their models look like they were originally scanned from small sculptures -- although in this day and age, it's possible they were just created as 3D models in the first place.