The parent is correct, the claimed relationship being y ~ rank^a for some a<0. You would want to see a linear relationship on the log log plot. Another choice would be to examine the complmentary CDF P(X > x) and look for power law tails.
I don't really have time to do this because I'm supposed to be working on a paper about, wait for it, power laws, but I went ahead and re-plotted the data using log-log axes. Sure enough, it's linear as would be expected for power law type behavior: