I'm not sure what point the author seems to be making about the DSM. They seem to be stating something along the lines of "The DSM isn't successful because it's atheoretical, it's successful because it adopted a biological theory, and because its emphasis on reliability facilitated sociopolitical control by the psychiatric profession." But later they recognize that the DSM isn't successful, seeming to contradict themselves.
The theory of the DSM goes far beyond biology, being explicitly neo-Kraepelinian and to some extent psychodynamic in nature, although that would probably not be acknowledged by any of the DSM's authors unless you pressed them on it. The success and failure of the DSM has everything to do with sociopolitical factors and the biological and nonbiological tenets of neo-Kraepelinian classification, and not on "atheoretical versus natural" or "scientific versus nonscientific" or "ontological versus nonontological" or "descriptive versus theoretical" or "ontological versus epistemological" or any of those sorts of distinctions.
The DSM adopted Kraepelinian categories and assumptions, shoehorning psychodynamic theories into this framework in some cases, and then further elaborating the system with very biological criteria. It essentially asserts that the major Kraepelinian categories are valid, that mental illness is discretely distinguished from normality or wellness, and that its categories reflect disruptions of biological systems that can be determined by certain patterns of biological observations. It further asserts that reliability is a central feature of classification and assessment. Some of these assumptions have been accepted, cementing its success, but some assumptions have been rejected by the community, leading to the current crisis that the author recognizes. Underlying all of this are sociopolitical factors, such as professional practice conventions, boundaries, and laws, and popular perception, that have both augmented the DSM, but also undermined it by highlighting the political processes underling its continued use.
The question is not whether a classification system is atheoretical or natural, or descriptive versus natural, or ontological versus epistemological, it's what criteria or theoretical principles are used to derive the system. In the case of psychiatric classification, the tension historically, even with the DSM itself, has not been about "atheoretical" versus "natural" systems, it has been about whether classification systems are at the level of behavior, which is proximate to the phenomena of interest and relatively tractable, or biology, which is proximate to the causes of those phenomena, but relatively intractable due to those causes being unknown. It's a bit like trying to classify species, genera, etc. without knowledge of genetics. You can proceed with a biology-based classification system under the assumption that your understanding is close enough, or you can acknowledge that you don't understand it and rigorously classify lifeforms based on what you do understand. Or you can try to do something intermediate. None of these are "natural" or "atheoretical," they're just at different levels of analysis. Another analogy might be found in computer science: do you derive document/file ontologies based on biology, or something like unsupervised AI classification? People like to assume that going down to a lower level of scientific analysis is always better, and it might be, but it might also not be, depending on your goals.