There is a difference between "appeal to nature" and the idea that there may be more compounds and nutrients in whole foods, perhaps acting in tandem, in ways that we haven't yet figured out.
I don't think this article is particularly well written or argued, but at the same time, I don't see any appeals to animism or mysticism in it. The author is simply suggesting, albeit not as clearly as he could have, that we have focused in isolation on only a subset of the nutrients we actually need. Obviously, the responsible "next step" to that sort of argument would be to form hypotheses and undertake further study. But that's not really the function of the article, as far as I'm aware.
Consider the broccoli example mentioned in the article:
"A 2011 study on broccoli, for example, found that giving subjects fresh broccoli florets led them to absorb and metabolize seven times more of the anticancer compounds known as glucosinolates, present in broccoli and other cruciferous vegetables, than when glucosinolates were given in straight capsule form. The researchers hypothesized that this might be because the whole broccoli contained other compounds that helped people’s bodies put the anticancer chemicals to use."
Now, the "appeal to nature" argument here would be that there is something fundamentally irreducible or non-replicable in broccoli that we just can't reproduce in a lab, because nature. That's not what the article says. Instead, it says that researchers hypothesized that there may be more components to broccoli than we've yet figured out. That's science. Science is always probing at the edges of what we haven't yet figured out, or revising what we think we have figured out.
The author does his point no favors by harping about synthetic vitamins. I'll grant you that. But he's not advancing any magical thinking.