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One of the main discussions in the paper is about the difference between arithmetic means and geometric means, and how people have different perceptions of annualized returns. Perhaps you should read it (again)?

It looks like they based it on the arithmetic mean of log-returns, which is equivalent to taking the geometric mean.

I don't see how that relates to the article?

The graphs are about long term returns. And how are those returns calculated? Because if they used arthritic mean, it’s overstating the actual annualized return.

Two things to note here.

First, it does not "overstate" the annualized returns. It just brings a particular view of them, which is the "expected annual return" vs the "compoundable annual return". Both are perfectly equivalent and represent different ways to look at annual returns. I would expect most practitioners to expect the former.

Second, this debate is completely irrevant here, as all charts show cumulative returns based on a $1 investment.