Tldr: dudes wife/kid die in an unpredictable accident so he builds a super computer that predicts things, and can even go back in time using probability. Interesting story.
That's not an unreasonable prediction but it's a little bit of a cop-out, especially the 51% bit.
Assuming that it gets anywhere close to that goal, does it take into consideration the effects of its predictions on the markets and calculates a fixpoint? (Or, maybe more likely, how the resulting chaotic system will behave?)
There is no tool that can do what this tool is claiming to do. At best, it can make reasonable inferences based on data it has available using whatever model it is using (assuming it's not a fraud) but key parts of the world are irreducibly complex. They cannot be predicted and that is without the problem of reflexivity which you correctly highlight as an issue - even for a notionally perfect prediction engine.
Given enough compute and data, you could model every human on the planet at subatomic granularity and you'd a) be chaotically sensitive to initial conditions; b) be subject to random quantum fluctuations.
Nice enough frontend though.
this is basically technical astrology.