Ya I really like this in concept. However, I think if you want to make a real go at it, and you want to use concrete, then I think a boom truck as they currently have, but with the 3D printing smarts to control the hydraulics and sensors to know where it is would be the way to go. With a nozzle of course.
But to be honest, I’m not sure that concrete is the right solution. For the size of the house that they built, you could build a traditional one just as quick at the same size. So other than being neat, I don’t see it being practical, really.
If you could print in both wood and insulation, then I think you’re getting somewhere. One nozzle can print structural wood mix, the other could print the insulation, both occurring for each layer with enough hardening time. Not sure how toxic smelling the end result would be. It might end up smelling like a big old mdf house.
Good luck doing more than one level though without using floor joists at least. You could design it to leave pockets for the joists, to be inserted later, and you could print the roof potentially depending on how much overhang the “filament” could handle.
There is an episode of Grand Designs where the university used a CNC in a shipping container to build interlocking wall assemblies CNCd from plywood, then filled them with insulation. That’s a nice idea.
You could also print the panels (be it foam or whatever) on location in the horizontal position, then allow some time to cure, then hoist into place.
I think a balance of customization and being practical is what you need to shoot for, personally.