I can think of several reasons for the article. Einstein was the first thing that came to mind, as he successfully posited an alternative to Newtonian explanations of gravitation (i.e. attraction as a result of curvation of spacetime), yet the author here does not adopt any of Einstein's ideas. Rather, Einstein would have prompted to the author to consider other explanations than traditional ones. And since Einstein was pursuing a unified field theory of physics in the 1930s, this may have suggested to the author that one major force of attraction (gravity) may be dispensed with. The analogy with the orbits of subatomic particles in an atom also may reflect popular understandings of advances of quantum field theory in the 1920s, which found new (weak and strong) nuclear forces.
More relevant is the discovery of Pluto in 1930. Neptune was discovered in 1846 on the basis of Newtonian mechanics with respect to perturbations in the orbit of Uranus, whereas another planet was suspected due to further disturbances unaccounted for by Neptune. The discovery of Pluto was announced on March 13, 1930 and this article in the Golden Age was published two years later, which refers to both Neptune and "the newly discovered planets", e.g. Pluto. I don't know why the author wanted to nullify the basis through which these planets were discovered, however.
I think another reason for the article is the old belief that God's home is in the Pleiades near Alcyone. That was based on a theory by 19th-century astronomer Johann Heinrich von Mädler, which claimed that "the star Alcyone -- the principal orb in the Pleides -- is at, or very near, the centre of gravity of all the stellar orbs -- the point around which the Sun and his innumerable companions are performing their revolutions. He tells us that as a consequence of his theory, the Sun's distance from the centre of his orbit is thirty-four millions of times the radius of the orbit of the Earth, and that the duration of this course is about 19,256,000 years" (John Nichol, Cyclopaedia of the Physical Sciences, 1860, p. 802). As his theory was presented by Pastor Russell, it was founded on a particular understanding of gravity: "Alcyone, then, as far as science has been able to perceive, would seem to be 'the midnight throne' in which the whole system of gravitation has its central seat, and from which the Almighty governs his universe" (Thy Kingdom Come, 1891, p. 327), and he found confirmation in a supposed correlation between the Great Pyramid and the star Alcyone. Since the teaching on the Great Pyramid bit the dust in the late 1920s, it is possible that by 1930, the belief about Alcyone also came under question, even though it is presented as fact in Rutherford's 1928 book Reconciliation (p. 14). It is curious though that the article nowhere mentions the Pleiades, despite the obvious implications in discussing the theory of gravity.
Finally, there was the discovery of Edwin Hubble who announced in 1925 that the universe is far larger than the Milky Way galaxy, which automatically would have cast doubt on older views like that of Mädler who assumed that the universe was only our galaxy. Then in 1929, Hubble formulated a new law of cosmology correlating redshift with relative distance, which further contradicted the steady-state assumptions of Mädler and supported Einstein's views. If the intent was to preserve Mädler's claims (instead of rejecting them), I would imagine that developing a different understanding of gravity than Einstein's would be one way of doing this. C. F. Stewart's focus on solar and steller light as "causing the rotary motion of heavenly bodies" may involve a misunderstanding of Hubble's redshift (i.e. light-spectrum based) evidence of stellar motion.
