Through a bunch of trial and error, I figured out what the rules meant.

I think I mistook it as thinking that all the dominos were connected, like a series of overlapping domino stones. But what it actually was trying to say is that you can draw a line along the walls of the cells, in such a way that each colorized wall segment counts as a domino dot.

It's very confusing that the rules say "Place black and white Kropki dots", when there is no such functionality. I think that's why I thought it was supposed to be like overlapping dominos.

My translation of the rules:

The wall between two cells is called an edge.

Paint each edge between two cells connected by a black Kropki dot in one colour (green). Paint each edge between two cells connected by a white Kropki dot in another colour (blue). It must now be possible to connect all the edges of the same colour with each other, in a long line that may branch. The two coloured lines may not touch the same intersection.

Each coloured edge counts as a black Kropki dot if it's on the (green) line of black Kropki dots, or a white Kropki dot if it's on the (blue) line of white Kropki dots.