I don't think it's the same as the fallacy of the beard when there's no continuum between the two examples, which will always be the case if the analogy between them is false. If it is the case that globalization is really just an extension of trading between hunter-gatherer tribes, then I agree with you. To me, they're two different things. If I take my glasses off and squint, they sort of look alike in a poetic way, but they're not actually the same, differing only in scale.
To me it seems like the author is stating a true observation, but they are ignoring the pace at which the phenomena is evolving given the technical advances mentioned in the article, especially of transportation and communication. The pace of cultural change matters greatly as large, quick shifts in culture are usually accompanied by massive resistance/wars, increased racism, genocides, autocracy, and a general desire to slow things down no matter what it takes.