First, the 'On the contrary...' in the article is not a rebuttal to the specific objection but a quote from an authority (Aristotle) supporting his general position. His specific rebuttal distinguishing the senses of 'natural' is later in that article.
Second, the soul is not, on the Aristotelian-Thomistic thesis, a "supernatural" being, as an angel or God would be since (though not material themselves) they properly belong to the material order.
So these are natural, not supernatural explanations, which nevertheless go beyond the purely material (corporeal) and so are 'above' them. In the quoted article, he means that these characteristic activites of living things are not simply reducible to those of the material parts themselves, since the living thing possesses the principle of its own organization/growth/reproduction etc. that non-living material does not, so something beyond the non-living 'corporeal' order must be operating.
Modern physics and biology really do not conflict with the classical Aristotelian-Thomistic conception of the soul but only describe in further detail the operations of the body.
The immateriality of the intellect is included there. Aquinas would say it is only the intellect that can understand a universal concept, which is itself immaterial. This is a qualitative, not a quantitative difference from the capabilities of AI. It is really the reductionists who are guilty of 'woo' here.
Second, the soul is not, on the Aristotelian-Thomistic thesis, a "supernatural" being, as an angel or God would be since (though not material themselves) they properly belong to the material order.
So these are natural, not supernatural explanations, which nevertheless go beyond the purely material (corporeal) and so are 'above' them. In the quoted article, he means that these characteristic activites of living things are not simply reducible to those of the material parts themselves, since the living thing possesses the principle of its own organization/growth/reproduction etc. that non-living material does not, so something beyond the non-living 'corporeal' order must be operating.