No, and please don’t try to learn anything from that science-free series. The author doesn't even have a Wikipedia-level understanding of what he is writing about.

N-body problems for N>3 do not have exact, closed form solutions. For N=2 the solution is an ellipse. For N=3+ there is no equation you can write down that you can just plug in t and get any future value for the state of the system.

But that is NOT the same as saying it is unpredictable. It is perfectly predictable. You just have to use one of the many numerical solutions for integrating ODEs.