From the article : "The sequencing of the pictures on these trials was randomly determined by a randomizing algorithm … and their left/right target positions were determined by an Araneus Alea I hardware-based random number generator."
At the very least they were using Araneus Alea wich is a hardware random number generator, so the numbers were not predictable. It's possible that the "randomizing algorithm" did something dumb and made the sequence not random, but I doubt it.
I think that it's more likely thet the sudy was done so many times that it eventually gave significant results than it is that the sequence was not random. Or maybe prescience is real to some degree, or the study is a statistical glitch.
However the replication package they provide has the compiled program without the source code, and that is a red flag to me.