The "butterfly effect" is only possible in some classic systems. For example imagine that you put a drop of ink in a glass of water (with some sugar). If a butterfly drinks some water, it will not change the final equilibrium state where the ink is evenly distributed.

This prove that one particular quantum system does not have an important butterfly effect, not that any quantum system does not have a butterfly effect.

(Note that r(as far as we know) reality is described by quantum mechanics. So it they prove that any quantum system does not have a butterfly effect, then the weather and all the other macroscopic systems do not have a butterfly effect.)