Perhaps some ancient ones, but also more modern historians. When this list was written almost 50 years ago it seems that tradition was already fading, and now...as far as I can tell...it's covered in dust. Old histories inevitably contain aspects we find mistaken (both morally and factually). But I personally love reading them for the strange perspective, the vigorous speculation, the calm judgement.

Gibbon was surely intended as a "Great Historian". And Macaulay (whose "Third Chapter" on the history of the people of England inspired generations of scholars). Maybe Michelet. Prescott. You can still find these all the time in battered Modern Library editions in used book stores.

For my money the greatest historian (who was surely meant) was Jacob Burckhardt, not-quite-incidentally a student of Schopenhauer and friend of Nietzsche. A modern edition will use footnotes to correct claims that turned out to be errors, and you're left with an elegant, sweeping vision of human activity, saturated with all the melancholy and resignation appropriate to the subject.

Two early twentieth century books I've read that probably fit the mold of "great historian" intended by this author are Webb's The Great Plains and Young's Victorian England: Portrait of an Age.

I think what the author means by "old great histories"---as distinct from the many old "scientific" histories that are now merely wrong---is that the historian takes human nature as the primary subject and uses historical fact, at least as best as can be ascertained, as the concrete medium for both exploring and shaping it.