Stereolithography is horizontal, one layer at a time, and uses photopolymerization (that's Formlabs). (Also Digital Light Processing is close but distinct: https://formlabs.com/blog/3d-printing-technology-comparison-...)
Continuous Liquid Interface Production (CLIP) also uses photopolymerization, but pulls the object from a liquid bath and uses a buffer zone. Still horizontal slices. The upshot is it's much faster. (Carbon 3D is the company behind this.)
The method in the article uses photopolymerization to solidify the object as a set of slices, but the slices are not horizontal.
The big drawback to photopolymerization is it only works on certain resins which can often have undesirable mechanical properties (high elasticity or brittlness, for e.g.) Potentially this method could be a way forward in that respect, because you might be able to put structural materials in the resin solution and end up with a composite. It seems easier to do this way than with CLIP or SLA/DLP, but I'm purely speculating.