Parler itself must expose a way to download posts and associated files. The hacker took advantage of this.
I believe the Parler CEO was able to download all of President Trump's tweets from Twitter to make it easy for him to migrate to Parler, so many social media sites provide this capability.
I doubt if much will come of this ... just a guess.
That was actually the CEO of Gab that did that.
I think it was Gab, not Parler, that downloaded all Trump’s Twitter posts to make them available.