The 1830 typesetter treated “that spiritual death” as connected with the following text rather than as an appositive that restates “the first death”. He placed a semicolon after “the first death” and no punctuation after “that spiritual death”. For the 1879 LDS edition, Orson Pratt redid the punctuation in accord with the more appropriate reading, replacing the 1830 semicolon with a dash and inserting a semicolon after “that spiritual death”. A similar kind of appositive usage occurs later in this same chapter:
In this second example, the text renames “a spiritual death” as “a second death”; this interpretation is facilitated by the use of the yea, which makes the appositive relationship clear, unlike the case in verse 16.
Summary: Accept Orson Pratt’s 1879 change in the punctuation for Helaman 14:16 that leads to correctly interpreting “that spiritual death” as an appositive describing “the first death”.