No, that's my bad, thank you for correcting me! I only read the abstract, and they don't mention Bayesian methods there. Confidence intervals suffer from similar flaws as p-values and statistical significance.
It's great that they do analyses with other methods too indeed. Not, from my point of view, because they're more approachable – quite the opposite: people think in terms of probabilities-of-the-hypotheses, and p-values are not that (that's one source of their misuse). But because it helps the transition to other methods. It'd been nice if they had stated the results from all methods in the abstract. But that'll be for next time maybe!
Maybe there's some problem with the links? If I click the image or the title of your post I only get redirected to an image.