I think the theory for the normal orbit is that the force given by Newtonian gravitation points outward rather than inward, but then the effect of an outward-pointing force on an object of negative mass is to cause an inward-pointing acceleration.

As other people have pointed out, that's inconsistent with other aspects of the simulation, and maybe just means that the author happened to use two equations involving mass in the simulation and the two negative signs cancelled each other out. Whereas using an odd number of equations involving mass would cause a physically noticeable different result.

I actually wonder if one could derive an explicit contradiction in Newtonian dynamics by allowing negative masses. That is, show that there is no trajectory that actually satisfies all of the equations in this case. (But that might also depend on which equations we think are fundamental. E.g., if we break conservation of energy, is that just an interesting consequence that that law doesn't apply anymore, or is that a contradiction?)