The author is truly out of his depth and it is embarrassing that he could not be bothered to research the various conceptions of the "soul" that exist in the philosophical literature, given that his very field takes its name from the Greek name for soul, "psyche" (ψυχή).

The popular view of the soul today is indeed strange. It has a Cartesian flavor, some kind of ghastly thing, perhaps some kind of ectoplasm, haunting a corporeal body or something like that. This is not the traditional view held by Aristotelian/Thomistic philosophers or theologians. Their view can be summed up with the following statement:

The soul is the form of the body.

Thus, what we call the soul in this regard is but the thing that causes a body to be what it is, namely, its form. By analogy, the form of a bronze sphere is its spherical shape. Pound the ball with a hammer into a cube and you've no longer got a bronze sphere.

Now, in the case of rational animals, I'll have to correct you somewhat. The immortality that Aristotle and Thomas are talking about is due to the intellectual and volitional faculties that such animals possess. Because we are capable of abstraction, the intellect must be incorporeal as abstraction involves the consideration of form apart from matter. But matter joined to form (as it always is "out there") always results in a thing that is of the kind as determined by the form; you will never encounter triangularity "in the wild", only concrete triangles. Matter is the principle of individuation. Thus, for form to exist by itself, there must be something immaterial in which it must inhere. Hence, the intellect is immaterial. And because matter is the principle of change, and form is not, only matter is corruptible, because it is subject to change. Therefore, the intellect as such cannot die. Thus, in rational animals, death is more like an amputation of the body rather than annihilation (non-rational animals simply cease to exist). Resurrection is, therefore, a restoration of the body to the person who has been truncated to mere intellect and will. But the intellect and will are not some ghost as the form of human beings is that of a rational animal. It is not as is the case for Descartes that the body and mind are separate things in their own right only incidentally connected in the way the driver of a car is only incidentally its driver. The intellect is a part, and the form is inherent to every faculty and thus your body is what it is as determined by the same form that determines the intellect as part. In short, you could not have had any other body than the one you have, or more accurately stated, you could not have been any other body than the body that you are, as you are every faculty and part that you are intrinsically by virtue of your form.

This will seem very difficult to grasp for those who have not encountered this before as it is very abstract and it does take time to understand the basic ideas. But the basic idea, that the soul is the form of the body, makes soul a kind of special case of form, the form of living things, and form is necessary for any identity and intelligibility. Everything is what it is by virtue of its form.

Some further reading [0].

[0] https://edwardfeser.blogspot.com/2012/03/what-is-soul.html