Thus, since the term "erets" can mean either the entire planet or a particular area, then the definition of the word in a particular verse must be based on its context.
...In fact, Genesis 2 begins with God planting a garden in a place called Eden, whose location is described in the text that follows.
...Thus, it is apparent from the context that when Genesis speaks in Genesis 2 of the fact that "no shrub of the field was yet in the earth, and no plant of the field had yet sprouted, for the LORD God had not sent rain upon the earth, and there was no man to cultivate the ground" in Genesis 2:5, it is referring to a localized area -- not the whole world. The localized area being referenced is the "land" where God was about to plant the Garden of Eden.
But this won't do. The word eretz does indeed indicate areas smaller than the cosmological earth, but almost without exception the reference is to large geographical or political areas. In fact the only example I can find of eretz applied to a small plot of land is in Gen. 23:15: "A piece of land (eretz) worth four hundred shekels of silver, what is that between me and thee?" (The other main usage of eretz is to indicate the physical soil itself.)
Therefore one would not ordinarily expect eretz to be used without qualification of a future garden site. Furthermore, as the writer notes, context is important in determining the range of reference; but he errs by saying that "Genesis 2 begins with God planting a garden." In fact, the section begins in Genesis 2:4b: "in the day that the Lord God made earth (eretz) and heaven." In such a collocation, only the cosmological earth could be in view. The sense of the eretz of 2:5 is thus established by the usage of eretz in 2:4, just as the sense of the same word in 1:2 is established by its meaning in 1:1.
The argument therefore fails. But what really troubles me is that such arguments still find a place in the apologetic enterprise. Apologetics is a worthy and important activity, but I regret that many of my co-religionists find it necessary to read and defend Genesis as straight, error-free, unedited reportage; and lurking in the background of this flat reading of the text is a "creationist"* (actually Young-Earth) account of cosmology. Fellas, that dog just won't hunt.
Nevertheless, it seems to me that a good design argument could be (and has been) deployed by apologists without reliance on a biblical exegesis that ignores the sciences of both geology and philology.
*The word "creationism" is now well established to refer to "Young Earth" theories, which strike me as a form of pseudo-science. Nevertheless, all Christians are necessarily "creationists" in some sense, if we take seriously the Nicene Creed ("creator of heaven and earth").