My mistake, you said "Classical Mechanics", so I took it as such.
But thermodynamics is not required either. Chaos theory would be of important note here. Take the double pendulum for example. It is a chaotic function because unless you have the initial state you cannot make accurate predictions as to its forward time evolution. This is a deterministic system because there is no randomness in the forward time evolution. But it is chaotic because it is sensitive to initial conditions. I think you can see that there's a careful choice of words here and that once we start trying to reverse the evolution we will not be able to do so. We have to deal with injective functions and I'm not sure many people really think P=NP. Just because f(t) has a unique map doesn't mean f^-1(t) does. Do not confuse "deterministic" with "predictable" nor "invertible" (nor "reversible" and "invertible"). Nor should you confuse "Newtonian Mechanics" with "Classical Mechanics".
Besides, I don't think you can throw out thermodynamics just so easily. With it you throw out many things like friction too. Not to mention that you're suggesting you're also throwing out fluid mechanics. For the fun of it, let me introduce you to Norton's dome since we might want to look at determinism in Newtonian Mechanics and a frictionless system ;)
Sorry, with all due respect, I'm not "throwing out" thermodynamics. It's just not relevant to the discovery referenced in the article, which is only concerned with classical mechanics. Thermodynamics is not part of the theory of classical mechanics. I think perhaps you are confusing classical mechanics with classical physics.
I've lost track of the point you're trying to make. Are you still trying to convince everyone that quantum mechanics and thermodynamics are part of the field of classical mechanics?
And yes, you're right, the article does mention this later. I'm still bothered by the sensationalized introduction and title.