Normally in the Book of Mormon we expect the relative pronouns that begin with wh (such as which and who) rather than that. Still, that does occur as a relative pronoun, though infrequently. And not surprisingly, there has been some tendency to accidentally replace actual cases of that with who or which. Here in Alma 62:27, the 1892 RLDS edition replaced the that with who, a change that was not reversed in the 1908 RLDS edition but has continued in the RLDS text. A similar example is found in the LDS text in a quotation from Matthew 7:13:
In this instance, the that is in the King James text, but the 1852 LDS edition has which, a grammatical variant that has persisted in the LDS text. There are also cases where the opposite change has occurred—cases where an original which has been emended to that (for an example, see under 1 Nephi 13:23). In general, the critical text will restore each original instance of the relative pronoun which, who, that, and so forth. For a complete discussion, see under which in volume 3.
Summary: In accord with the reading of the earliest textual sources, accept the infrequent use of the relative pronoun that wherever it occurs, including cases in Alma 62:27 and 3 Nephi 14:13.