A reader, Aryeh Mellman, has the answer:
John McWhorter’s new article on the disappearance of Aramaic, while fascinating, omitted a relatively small, yet substantial, subset of Aramaic users.
The Talmud, one of the foundational Jewish texts, is written in a mix of Biblical Hebrew, Mishnaic Hebrew, and Aramaic. To study this text in its original form, a number of Jews have familiarized themselves with Aramaic.
Studying Talmud in the original is mostly done in Orthodox circles (both Modern Orthodox and Haredi), which comprise about 10 percent of American Jews—about 600,000 people. In Modern Orthodox schools (one of which I attended), Talmud, in all of its original and Aramaic glory, is studied for 1-3 class periods per day in middle school and high school (45 minutes-2.25 hours) along with secular subjects.
In Haredi schools, Talmud is studied for longer periods of time.
There is a tradition to study “daf yomi” (daily page), and every 7.5 years, all who have completed the entire Talmud by studying one folio per day for that time, flock to a public gathering place to celebrate their accomplishment. During the last celebration in 2012, over 90,000 participants packed MetLife Stadium in New York.
This is just in the U.S.; there are several hundred thousand, if not millions, of Israelis who also regularly study the Talmud in Aramaic.
So while McWhorter is correct that Aramaic may be dying as a spoken language, there are not insignificant numbers of people who continue to study Talmud intensively, and thus read Aramaic with relative frequency.