I haven't read Richard Schmitt which makes me hesitant to answer the question as to what he means, but I can address the quote and what Kierkegaard means.
First, the idea is not singular to Kierkegaard. It, in fact, traces back to Aristotle. For Aristotle, we are animals -- but we are animals who join to being animals some form of rationality. Being animals for Aristotle means that we are alive and that we have sensation and motivations. Being rational means that we are capable of acts of reasoning and of decision making (you can find these ideas in BK I of Nicomachean Ethics but also in many other places in Aristotle's corpus).
An important second idea is teleology, which is to say that for Aristotle (and at least to Aquinas), what we are to do is determined by our nature. (This is also discussed in Nicomachean Ethics BK I and BK X).
Modernity throws a wrench in the teleological aspect in at least two ways. It would take a book to discuss how in detail, but (1) the natural world is no longer explained in teleological terms on a regular basis (think Hume's denial of causation) and (2) the role of consciousness is raised (think Descartes' project in the Meditations and Kant's Critique of Pure Reason).
With this out of the way, we can finally look at Kierkegaard and what's going on here. There's a passage in Anti-Climacus's Sickness unto Death that deals with the aspect in which we are blessed/cursed to have to make choices by pointing out that as humans we are different from the animals in that we have to make choices and thus can experience despair.
Separately, there's a discussion in Concluding Unscientific Postscript that identifies eternal happiness as the end of man, which echoes the Aristotelian picture in its Thomistic modification.
To make that a bit more practical, a giraffe goes around giraffing. It has a "teleology" from its genetics that just make it behave giraffingly. It spends its time going around eating from tall trees and having a blast (predation excepted). Maybe it picks to go for tree #1 or tree #2 based on which thing it likes.
Humans, in contrast, have so much capacity that we can question our own goals, motives, and capacities. In other words, we have to make choices about what we will do and about what we will think is worth doing.
The thing which forces this on us is that we are rational in addition to being animal. This means the pre-programming of what we can do is controlled by our ability to pick some of our ends. Obviously, this occurs within some limits, but the basic point is that I can, unlike a squirrel, decide that the purpose of my life is to collect sailor moon goods and devote myself to that whereas a squirrel just squirrels. Moreover, we are underdetermined in ends to a sufficient degree that we must pick.
The above paragraph is basic existentialism, but Kierkegaard's particular take is not that we are without ends altogether (as one might find in Camus) but that we face the challenge of rationally appropriating our ends whereas most animals don't (I can't vouch for whether the author in question understands Kierkegaard in the same way on this point as I do).
It's also worth noting that this idea of humans being different from animals in having reason is not singular to Kierkegaard. In fact, Hegel shares it and specifically links it to an account of necessary fall vis-a-vis the Garden of Eden (Encyclopedia Logic ยง24 Zusatz).
