Remember quantum mechanics started with the Bohr atom which was an approach that would generalize to any system that has quasi periodic (solar system in the short term) dynamics. Circa 1917 Einstein wrote a paper that said that this approach wouldn’t generalize because Poincaré proved that chaos is generic, soon after that we got Schrodinger’s equation and similar approaches. (Although that Einstein paper killed a line of development it barely got cited for 50 years)
Later on there were mathematical developments in quantum chaos such as Gutzwiller’s trace formula and also numerical work where people discovered various properties of the quantum levels of systems that were classically chaotic.
Linear operators in quantum mechanics don’t precluded observing chaos in the real world because the true “long term” is very long indeed. That is, classically or quantum mechanically if you wait some really absurdly long time (say much more than 10^120 years) the universe is expected to come arbitrarily close to the state it is in today. See
https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theor...
The article implies this is what was proved, but later contradicts itself. Based on my reading, only a couple specific initial conditions were proved to be unstable.
The first paragraph of the linked article talks about simulation experiments from 2009, so your criticism here that there is some spurious claim to novelty is pretty unfounded. Simulation runs that show instability are old hat; mathematical proof that this instability is inherent and unavoidable is the story.