A very difficult part is weight distribution, balance, and having some kind of support system to hold it in place as each rock dried on to the other. I think it would work with any kind of flat rocks, though the polished roundness is pretty. I just don't know what adhesive would be best. It would be great to have a permanent weatherproof fast drying adhesive, but I don't know of one.
I tried a version of it with small rocks; that's how I know of those particular problems. You have to prop it up as you build it and E6000 and the silicones don't dry very quickly.
You could lay each rock on its side on a flat surface and build it horizontally, then upright it when dry, but it would have to be anchored into a substantial base to stand upright, otherwise the weight would have to all be in the bottom.
Ask me how I know all this. Ugh.