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Is this really new? IANAP, but I clearly remember being taught about the Arrow of Time as a probabilistic/thermodynamical phenomenon even in high school and I also read similar explanations that involved causality and probability theory without refering to quantum entanglement. Is the "quantum" bit even needed there for anything?

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Probability theory is how we model the arrow of time, but it's not a physical mechanism by which the arrow of time occurs. The article covers this distinction.

Isn't the classical definition of Arrow of time is from the system with less entropy to a system with more entropy? What is lacking in this definition of Arrow of time that we need to take it to Quantum level?

How the entropy spreads on a microscopic level, rather than a statistical one.

Again, probability is just a model that can predict something, but not explain how it works. Take a pseudorandom number generator and do rand() > 0.5. Your probability is 50%, and that is a pretty good model to predict how the subroutine will behave, but it may also be useful to understand what algorithm the PRNG is using.

In physics, a "model" is the same as "how something works", unless and until you can uncover details (like the precise order of generated numbers) that the old model can't express.

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