It takes a while and you might be mislead to thinking nothing was done, depending on how you monitor the reported games. You will never get an answer to your reports. And they might stay quite a while in your watchlist if you put them into a collection.
But itch does not enough in regard to piracy.
All tickets below reported over a month ago. All still downloadable. All provided with source of original paid work. Oh, they are quarantined, but you can still download them - which is what I meant with not enough. If the game can still be downloaded, you can still advertise them on message boards, discord and so on. And judging from the file sizes of the downloads, some might even be tampered and contain malware.
This thread adresses this very problem with the direct links advertising. Thanks for pointing that out. Maybe itch does not think about that possibility, because they only quarantine some of the games. And you only notice that, when you click the download button.
R-59558 . A paid game from DL-Site
R-59580, also DL-Site.
R-59602, the account has 3 pirated games on their profile. For one the original is on itch, no less.
R-59560, on steam.
Tbf, most games I reported are gone. And I think I reported one game that might or might not have been put here by the author, so not being too hasty is prudent. There are lots of creators putting a free version on itch, after all. But I doubt one can find creators selling on dl-site doing that very often.