This passage involves the deletion in the 1837 edition of the repeated pronoun he. This kind of editing also occurred earlier in this chapter (see 1 Nephi 2:4, 7). But in this example the second subordinate conjunction that was also edited out. This editing is consistent with the deletion of the first that in this verse. In his editing for the 1837 edition, Joseph Smith fairly consistently removed that whenever it was immediately preceded by because, so it seemed appropriate to remove the that both times from these conjoined clauses. For further discussion, see subordinate conjunctions in volume 3.
Summary: Based on the earliest textual sources, the repetitive subject pronouns in conjoined clauses should be restored in the critical text; coordinated uses of that following another subordinate conjunction (like because) should also be restored.