The article is pointing out that, if we think of Newtonian mechanics as a set of math equations, then there exist simple systems in which the future of the system has multiple equally-valid solutions to those equations.

Mathematically, it’s possible to have a differential equation with an initial condition, and still have multiple different solutions. That’s what the author creates as well.

I don’t think this article is about continuous vs discrete physics, as some commenters suggest - nor about reality at all (not directly). Rather, this is pointing out a surprising property of the model of Newtonian mechanics.