Try looking past the synopsis
The ironic thing is that those guys were looking for cyclical phenomenon, and so they "detrended" the data: "Regardless of source, the ultra-low frequency variation is removed prior to the analysis". They were looking for cycles of a decade or less, and removed any longer-period variation.
Look at their Figure 1, raw data before "detrending". The caption says "Note the low frequency change in annual abundance over the 111-yr period."--the change they're talking about is positive. If I'm reading this right, they found, but removed, a longterm trend showing an increase in hurricane frequency.
In other words, they were specifically not taking the long view.