What does it mean for Einstein's equations to 'emerge' from rewriting?

The proposal is that Einstein's equations are not written into the rewriting rule. Instead they are claimed to show up only when you zoom out: the curvature read off from how fast hypergraph neighbourhoods grow, averaged statistically over large regions, is argued to obey the same equations Einstein wrote down — much as the smooth laws of fluids emerge from countless colliding molecules. This is presented as a large-scale, statistical limit of the model, and the rigorous version is admitted to be unfinished.