In the article by A. Douglas Stone we read (at page 2):

As long as the force law is not exactly proportional to 1/r2 or r, the mass’s orbit will typically not close on itself: In astronomical terminology, it will precess;

The same is true when the force is proportional to 1/r2 but does not point to the center of mass of the first object using Newton's Law.

Einstein would have been aware of that fact from his work on the relativistic theory of the precession of the orbit of Mercury!

Exactly also true using Newton's Law.

Equation 4 says that quantization is achieved by setting 2 * pi * L = n * h.
In other words, L = n * h', the familiar Bohr rule for the quantization of angular momentum for
an arbitrary central force law. The second loop integral will quantize the energy of the motion and its precise form will depend on the particular force law.

The simplest case is that n=1. What does this physical mean? Is this the energy of a photon? of a certain frequency?
At page 3 we read:

physicists now understand that integrable systems are highly exceptional and that the generic case — the nonintegrable system — always has some regions of phase space where the dynamics are chaotic, that is, where trajectories are exponentially sensitive to initial conditions.

Generally speaking all processes are sensitive to initial conditions. It is an exception when this is not the case.
But there is more. All processes are also sensitive to additional process parameters, which are often unknown.
One example is for example friction. If you place a ball inside a torus and you give a ball a reasonable speed the outcome is completely unpredictable at which position it will come to rest. The reason is friction.
In the paragraph A modern perspective we read:

To clarify the relationship between Einstein’s type (a) and type (b) motion and what is now called regular and chaotic motion, one can turn to dynamical billiards, which are paradigms for the study of classical and quantum chaos.

You can ask you self the question what this has to do with the quantum theory.

Figure 3. Billiards. (a) Generic trajectories in a circular billiard are quasiperiodic.

The problem with all 4 examples is that they are artificial because no friction is included. When friction is included they all become indeterministic.

Figure 5. Chaotic wavefunction of the stadium shaped billiard.

This is a typical artificial problem. The reality does not show this behaviour.
The article ends with the following sentence:

Although Einstein’s antipathy to certain aspects of modern quantum theory is well known, there appears to be a renewed appreciation this year of his seminal contributions to quantum physics.

Unfortunate in this document those aspects are not mentioned nor is there an indication if Einstein was right.

With his introduction of the photon concept in 1905, his clear identification of wave–particle duality in 1909, his founding of the quantum theory of radiation in 1916, and his treatment of the Bose gas and its condensation in 1925

This list identifies Einstein's huge contributions to the Quantum Theory and the fact that he did not agree with other issues, with which he was propably right, made him a giant in physics.

Reflection
One of the most important questions to answer is: How important is this document? How important is this concept of quantification?
Niels Bohr introduced in 1913 what is called The Bohr Model (Wiki) . Together with the Rydberg formula gives this a good description what is happening at atomic level. The period before 1925 is called the Old quantum theory (Wiki). The article by Douglas Stone falls (partly) in that cathegory.
After 1925, influenced by Erwin Schrödinger (Wiki) (Schrödinger equation) the quantum theory Quantum mechanics (Wiki) was develloped.
In the document: Schrödinger equation  Historical background and development (Wiki) You can read:

Schrödinger, though, always opposed a statistical or probabilistic approach, with its associated discontinuities  much like Einstein, who believed that quantum mechanics was a statistical approximation to an underlying deterministic theory — and never reconciled with the Copenhagen interpretation.

The problem is experiments and observations versus mathematics.
When you study the Rydberg formula, the Lyman Series, the Balmer Series etc you can see that observation and mathematics coincide.
For the Schrödinger equation (which involves complex numbers) this is much more difficult. It seems that the theory only can be tested for very simple examples.
A second problem is the sentence: "quantum mechanics was a statistical approximation to an underlying deterministic theory "
IMO this is not correct. IMO:

"quantum mechanics is a statistical approximation to an underlying indeterministic world and only for simple situations"
The same problem exist also with QBits and superposition. You can write a thick book with mathematics using QBits and quantum logic gates, but if there exists no good way to test the input and output of the experiments using QBits than what is the importance of all of this?



