"Our sales data are provided by two major U.S. movie studios and include all digital purchases and rentals through their major digital channels aggregated at a weekly level from September 2, 2011 until May 31, 2012. These data include each of the 12 countries where these digital channels were available as of September 2011."
Quote from page 8 of the paper (First paragraph of section 4 if you care to look it up in context).
My concerns are that (1) the study was funded by the same individuals who provide the data showing immediate conflict of interest and (2) the data does not span a 12 month spread. So even though they claim to make consideration for seasonal attributes like Christmas sales we don't have a full data set to know if the rise/fall pattern they display is typical for this timeframe. The release of "summer blockbusters" or other studio phenomenon cannot be compared to the data unless we have data spanning multiple years to know when peak seasons of sales are.
Heck, a third issue is their lack of physical sale data. So although they have source showing digital piracy to digital sale correlation is likely it doesn't account for digital adoption of newcomers to the market.