Seems like an extension of work by Judea Pearl (the graphical models in the blog's first figure is a dead giveaway), which requires knowing certain assumptions about the data. Not sure I'd call it "revolutionary" as there is a ton of work in this direction (much of it cited in the pre-print).
Specifically, note from the pre-print this limitation, so it's not really the causality that most people have in mind when they think they have proven cause and effect (intervention is still the only way to really determine cause and effect without redefining causality or making tricky assumptions about the underlying causal model):
In this work, we will simplify matters considerably by considering only (a) and (b) in Figure 2 as possibilities. In other words, we assume that X and Y are dependent (i.e., PX,Y 6= PXPY ), there is no confounding (common cause of X and Y ), no selection bias (common effect of X and Y that is implicitly conditioned on), and no feedback between X and Y (a two-way causal relationship between X and Y ). Inferring the causal direction between X and Y , i.e., deciding which of the two cases (a) and (b) holds, using only the observational distribution PX,Y is the challenging task that we consider in this work.
