Hey, I just found your post after watching the two videos you linked. I am not sure if terraponics is a rebranding of other techniques or a truly new way to do things. On one hand seems a complicated wicking bed (pipes, pumps, filters?). On the other one seems an ebb and flow hydroponics (note that people have been growing soil plugs in clay pebbles for ages). I still don't know where the nutrients come from, soil or added with the water?
I don't see any advantage over a wicking bed system, besides potentially reducing the weight of the whole contraption. But if you are going to have pipes and pumps, you can do a wicking system with small reservoirs.