I'm trying to say this with as little judgement as possible. I just know that deciding to look only at certain countries to support a hypothesis has been done before (c.f. Ancel Keys's Seven Countries Study).
I've not read the paper so I've no idea if this is an issue or not, but only using the data of two studios seems to be a low sample size.
Imagine if the week after the shutdown "Lord of the Rings" was released, or "Twilight", or any other blockbuster. Find two studios with big releases in the period after the shutdown and it looks like some significant causation.
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.