I don't find the "autocorrelation" explanation intuitive (although it may be equivalent to what I'm about to suggest). The way I think about it, is that it comes about because the y-axis is a percentile rank. How does it actually work for people to give unbiased estimates of their performance as percentiles? For the people at the 50th percentile in truth, they could give a symmetric range of 45-55 as their estimates, and it would be unbiased. But what about the people at the 99th percentile? They can't give a range of 94-104, the scale only goes as high as 100. So even if they are unbiased (whatever that means in this context), their range of estimates in percentile terms has to be asymmetrical, by construction. So, even if people are unbiased, if you were to plot true percentile vs subjective estimated percentile, the estimated scores would "pull toward" the centre. Then the only thing you need to replicate the Dunning-Kruger graph is to suppose that people have a uniform tendency to be overconfident, i.e. that people over-rate their abilities, but to an extent unrelated to their true level of skill. The estimated score at the left side of the graph goes higher, but it can't go as high on the right side of the graph because it butts up against the 100 percentile ceiling. Then you end up with a graph that looks like lower skilled people are more overconfident than higher skilled people are underconfident.
It's an interesting article but the author is using terms a little incorrectly or strangely I think, and making untrue statements. The basic points are important and interesting to think about, but could've been explained more clearly.