The very short answer is "no". Neither the article, nor physics, rule out the existence or agency of Gods.
Somewhat Longer Answer:
The author is trying to stake out a very peculiar position. Most Anti-spiritualists assert ONTOLOGICAL naturalism -- I.E., that there is no such thing as non-material. They generally concede that the methodologies of science and reasoning, which combine to form methodological naturalism, could be used to investigate whether spirits influence our world.
This author seems to have put himself in a box, however. He WANTS to assert Ontological naturalism, but admits that the test cases of abstract objects -- Poppers World 3 -- exist. He also admits that minds exist, and that he cannot rule out that they are world 2 rather than world 1 objects.
This leaves him searching for a justification for his belief in an effective ontological naturalism, and this effort to redefine methodological naturalism to exclude certain categories of hypotheses, is a very blatant kluge/rationalization. Note how he describes it:
it would be a mistake, I think, in the present context, to bind naturalism to a
commitment that minds are material. That is arguably not something that science alone can settle, but however it is settled, we should not hold psychology
and the social sciences hostage to the outcome. Thus I propose that the right
sort of gerrymander here, to give us what matters, is one that rules out disembodied minds. Naturalism, then, is committed to there being none of those.
Note he admits up front, that he is "gerrymandering" the normal usage of methodological naturalism, to try to prevent study of subjects he wishes were not the case. The methodology of naturalism is not committed to excluding acceptance of certain answers of "what is our world like". His admission that whether minds are material or not is an open subject, but that he is ALSO excluding trying to answer this open question from any kind of scientific inquiry, shows exactly what this sort of ideological effort to constrain science leads to.
In prior centuries, the Church, or the Commissars, banned study of certain subjects because they contradicted their ideologies' dogma. Evan Fales is trying to do the same today.
Even More In Depth Answer
Fales makes an implicit assumption about science, and physics laws -- that science laws are ABSOLUTE LAWS, not regularities. This is clear in his discussion of conservation principles. But this is not how laws work in science. Laws are regularities. They do not always hold. A good discussion of how all science laws break naturally is in this paper: https://www.pnas.org/doi/10.1073/pnas.93.25.14256
Not only are conservation laws not absolute, but causal closure for the physical is not a valid assumption either. First, it is simply inconsistent with science as an active and open field of inquiry. So long as we are still doing science, current science cannot be closed, and future science cannot exclude any logically possible causal paths.
Further, physicists do not treat causal closure as absolute, and cannot. It is not difficult to find examples of this. First, it is not possible to have any isolated system within the universe, as fields (gravitational, E-M) from outside will always cross any boundary. Hence one cannot have causal closure even within physics for any minimal physical system, other than our entire universe.
And for our universe as a whole, cosmologists basically have rejected causal closure. Whether it is the continuous matter generation of the Steady State Model, the spontaneous oscillatory excursion of "the equations don't exclude this" of low odds finally creating a universe from a void, the bouncing interaction of two adjacent brane-world universes, or the spontaneous spawning of baby universes in a multiverse universe -- cosmologists don't restrict themselves to conservation laws OR universes being causally closed.
Fales would have to say that cosmologists are not doing science, and banish them from the AAAS...
Aside -- Hoyle tried to find away to tweak the definition of conservation of energy to fit his model inside of it, and some Big Bang cosmologists have tried to do the same to say the spontaneous appearance of our universe in an instant did not violate COE. For a discussion of these efforts, and what they mean for COE and spiritual interaction, see this question and answer https://physics.stackexchange.com/questions/494408/the-zero-energy-hypothesis-and-its-consequences-for-particle-creation-and-dualis
Note that expanding the "system" (to include consciousness, or Gods) and asserting a new term that is still conserved in the larger system, is a typical strategy that has been used in many of these past speculations.
And second, "matter" is only about 5% of the known energy of the physical part of the universe, with the rest in poorly or non-understood dark matter and dark energy. And finally, unless one is claiming that all subjects reduce to physics, and Fales explicitly rejects that, then real events and phenomena are characterized in disciplines OUTSIDE physics, and therefore physics CANNOT be closed to non-physics phenomena.
As a further challenge to fixed laws -- the current understanding of the Cosmological Constant is that its value is set by the energy of virtual particles, and the energy of these particles comes from the "laws" and constants of the standard model of quantum mechanics.
But our Cosmological Constant was very large in the first instants of the Big Bang, and it is changing today. So -- these "laws" have and are continuing to change.
Referring to the title of your reference -- Karl Popper defined pseudoscience as the act of claiming to be doing science, while rejecting the possibility of refutation.
Naturalism is, per the author here, the belief that consciousness, or any world 2 object like a God, cannot causally affect the physical world. Your author is trying to redefine science, so that any examination of the possibility of spirit causation is not allowed as a scientific inquiry. IE that his view of naturalism cannot be refuted by science. Popper would label your author an advocate of Pseudoscience.