In this passage the editors for the 1920 LDS edition changed the singular record to the plural records, probably because of the plural are that follows. Although the clause “the record of our wars are engraven” leads to a grammatical difficulty, the plural are probably occurs in the original text because of the proximity of the plural noun wars. Such nonstandard usage occurred quite frequently in the original text. For a very similar example, see the discussion under 1 Nephi 13:23 regarding “a record of the Jews which contain the covenants of the Lord”. For additional examples, see the discussion under subject-verb agreement in volume 3.
An alternative grammatical revision for this passage would be to retain the singular record but change the plural are to the singular is: “for behold upon them the record of our wars is engraven”. Such a grammatical change, it turns out, is more consistent with usage elsewhere in the text. Whenever we have the phrase “record(s) of X”, where X refers to subject matter rather than to an individual or a people, we systematically get the singular record, never the plural records:
This systematicity suggests that in grammatically revising Jarom 1:14 for the standard text, editors should consider retaining the singular record and changing the verb form to the singular is.
Summary: In Jarom 1:14 the critical text will maintain the nonstandard “upon them the record of our wars are engraven”; the more appropriate grammatical revision would be to change the plural are to is instead of changing the singular record to records.