That authorship is one of two explanations offered by scholars
Rather than refer to a Christian source, an entry-level explanation of when Deuteronomy was written can be found at the Jewish Encyclopedia online site. (The unedited full-text of the 1906 Jewish Encyclopedia). The authors for this article are: Morris Jastrow, Jr., S. R. Driver, Emil G. Hirsch, Benno Jacob.
The author of the article you read was not making a definitive claim about authorship (his article was about books and book snobs, not about Judaism nor Christianity). He chose from one of the two options (see below) that scholarship has presented. Why he chose that is his own affair, but from the style of writing in that article, I'll offer that he made the choice for an artistic reason: it fits into the pattern of behavior he was building about 19th century and modern book snobs.
Note that "JE" in the text below refers to Jewish Encyclopedia.
Age and Authorship of Deuteronomy.
(From the Jewish Encyclopedia, see link above)
It is the unanimous opinion of modern critics that Deuteronomy is not
the work of Moses, but that it was, in its main parts, written in the
seventh century B.C., either during the reign of Manasseh, or
during that of Josiah ... {emphasis mine}
The reasons {evidence} for this conclusion, stated here in the briefest outline:
- Even upon the assumption that JE in Exodus and Numbers is
Mosaic,
the historical discrepancies in Deut. i-iv. and ix.-x., and the terms
in which incidents belonging to the fortieth year of the Exodus are
referred to, preclude the possibility of Deuteronomy being Mosaic
likewise; while the use of the expression "beyond Jordan" in i. 1, 5;
iii. 8; iv. 41, 46, 47, 49, for eastern Palestine, implies that the
author was a resident in western Palestine.
- The same conclusion follows, a fortiori, for those who allow
that
JE is a post-Mosaic document, from the fact, noticed above, that JE
itself, both in the narrative parts and in the laws, is repeatedly
quoted in Deuteronomy.
- In Deuteronomy it is strictly laid down that sacrifice is to be
offered at a single central sanctuary (xii. 5, 11, 14, etc.); whereas
in Joshua to I Kings vi. sacrifices are frequently described as
offered in various parts of the land (in accordance with the law of
Ex. xx. 24), without any indication on the part of either the actor or
the narrator that a law such as that of Deuteronomy is being
infringed.
- The other differences between the legislation of Deuteronomy and
that of Ex. xxi.-xxiii. point with some cogency to the conclusion
that
the laws of Deuteronomy originated in a later and more highly
developed stage of society than the laws of Exodus.
- The law of the kingdom (xvii. 14-20) is colored by reminiscences
of the monarchy of Solomon.
- The forms of idolatry referred to—especially the worship of the
"host of heaven" (iv. 19, xvii. 7)—point to a date not earlier than
the reign of Ahaz, and more probably to one in the seventh century
B.C.
The USCCB's (Conference of Catholic Bishops) on line version of the New American Bible offer this in the introduction to the book of Deuteronomy:
The book was probably composed over the course of three centuries,
from the eighth century to the exile and beyond. It bears some
relation to “the Book of the Law” discovered in the Jerusalem Temple
around 622 B.C. during the reign of King Josiah (2 Kgs 22:8–13). It
gives evidence of later editing: cf. the references to exile in
4:1–40; 28:63–68; 29:21–28; 30:1–10.