Asking a question about the foundations of statistical mechanics is a good way to start a fight, so don't expect a clear consensus on this.
Stripping away the hype, what these papers try to do is establish that an isolated quantum system will, under certain (but general) conditions, evolve to a state that looks like thermodynamic equilibrium locally, even though the system remains in a pure state and therefore, if taken as a whole, always has zero entropy. If you accept that the universe, or at least some subsystem, is fundamentally quantum mechanical and can be described as a closed system, then this is your ultimate explanation for how equilibration works. However, there are some clear logical leaps there that have not necessarily been worked out, such as whether this picture of spreading entanglement entropy is still a useful picture in a macroscopic, fully decohered system.
I would second CuriousOne in saying that the laws of statistical physics are ultimately rooted in probability rather than quantum theory, and in that sense are probably more fundamental than any other theory we have. It is no coincidence that our most secure beliefs about what quantum gravity says come from making it compatible with thermodynamics. Here is a very nice article from a little while back that gives a similar sentiment (paywalled, sorry). So I would agree that it is, at least, premature to claim that thermodynamics laws are ultimately a byproduct of quantum physics. However, the thermodynamics of isolated quantum systems is clearly a very important particular case.