I've only skimmed the paper so far, but apart from both using the word "emergence" I think you and the paper are talking about very different things. The paper

I've only skimmed the paper so far, but apart from both using the word "emergence" I think you and the paper are talking about very different things. The paper means something along the lines of "behaviours at different scales that are causally isolated from each other", and they give a mathematical treatment of that. I imagine they would agree with you that there's nothing magical about it! The map is not the territory but some maps are better than others.