The derivation they proposed—that the participle muʾarrakh, "dated", comes from the Persian māh-rōz, "month-day"—is incorrect.
Modern lexicographers have proposed an unattested Old South Arabian etymon for the plural tawārīkh, "datings", from the Semitic root for "moon, month".
The word taʾrīkh was never universal in the titles of works of history, which were just as often identified by subject matter (i.e., biography, conquests, etc.)
As its etymology implies, taʾrīkh originally described only a strictly chronological account, but it soon came to refer to any kind of history (e.g. historical dictionaries).
[1] The following are the names of prominent books with taʾrīkh in the title, in Arabic, Persian or Turkish.