Most of the examples in the repo have those NxN all one color patches. Or, without (C2) the algorithm would have generated completely empty integrated circuits, or completely grass terrain, which is really boring.
You understood right, it's constraints + probabilities.
I might try this approach to generate formal poetry -- it's something I've done by backtracking before, and I'd considered doing something like your ConvChain.
At first I thought that my methods don't offer anything new to text generation besides the Markov chain, but several people already proposed ideas that sound sensible, so let me know if you make anything!
You understood right, it's constraints + probabilities.
Btw, I have different algorithm that satisfies (C2) perfectly, but not (C1): https://github.com/mxgmn/ConvChain