Unfortunately, absence of evidence ≠ evidence of absence.
I obviously don't have time to read a 300 page report—I wish I did—but the conclusion says:
> With regard to total effects of online copyright infringements on legal transactions, there are no robustly significant findings. The strongest finding applies to films/TV-series, where a displacement rate of 27 with an error margin of roughly 36 per cent (two times the standard error) only indicates that online copyright infringements are much more likely to have negative than positive effects.
The conclusion goes on to discuss each type of media. Here's the section on games:
> For games, the estimated effect of illegal online transactions on sales is positive because only free games are more likely displaced by online copyright infringements than not. The overall estimate is 24 extra legal transactions (including free games) for every 100 online copyright infringements, with an error margin of 45 per cent (two times the standard error). The positive effect of illegal downloads and streams on the sales of games may be explained by players getting hooked and then paying to play the game with extra bonuses or at extra levels.
If this is what was meant by "illegal downloads and streams can actually boost legal sales of games" (and it's possible they're talking about something else which isn't in the conclusion), I don't find that convincing. It's within the margin of error and includes free transactions.
Moreover, I firmly believe that we are never going to have good data on this! You're trying to measure two things that are virtually impossible to measure with any accuracy: (1) how much piracy is taking place, and (2) what would sales have been without the piracy.
(I've edited my comment to actually quote the paper)