Here we have an obvious typo in the 1874 RLDS edition, the accidental omission of the second the in the phrase “the reign of the judges”. In this case, the 1892 RLDS restored the the to the RLDS text; the phrase with the the is so common in the text that the 1892 typesetter would have had no problem in deciding to add the expected the before judges. Theoretically, the the is not necessary, but elsewhere in the text there are at least 99 instances of “the reign of the judges” but none of “the reign of judges”. (Also see the discussion under Alma 10:6 for the phrase “the reign of our judges”.)
Summary: Maintain the the before judges in the phrase “the reign of the judges”, including here in Helaman 6:15.