I just had a brief look at the published version of the paper. Unless you work on fundamental aspects of quantum information theory, the actual implication is that some old debate that took place back in the 90s has been resolved. As others have already pointed out, the relationship between uncertainty relations and wave-particle duality intuitively makes sense, but actually coming up with a mathematical proof that the two concepts are equivalent to each other is certainly a non-trivial amount of work. However, this paper does not significantly change our understanding of quantum physics, nor does it allow us to magically find an efficient way to simulate quantum physics on classical computers. It will also not change the way quantum physics is usually taught, as wave-particle duality basically plays no role there (and uncertainty relations are mostly a side remark).

Also, notice that the paper has been published in Nature Communications. Usually, this means that the paper was rejected by Nature Physics (or any other of the "Nature Something" journals), so the authors sent it there instead (BTDT). So we probably have at least an editor (and maybe some referees) who thought that the paper was not as sexy as the press release seems to imply.