The original text here reads “built him an exceeding large ship”. The use here of the reflexive indirect object him is characteristic of the biblical style, with ten examples in the King James Bible, all of which refer to building a house, as in Genesis 33:17 (“and Jacob journeyed to Succoth and built him an house”) and in Acts 7:47 (“but Solomon built him an house”). There are also a few examples with the reflexive indirect object them, such as Nehemiah 12:29: “for the singers had builded them villages round about Jerusalem”. There is also one example earlier in the Book of Mormon text with him: “and he also built him a spacious palace” (Mosiah 11:9).
Here in the 1874 RLDS edition, the him was omitted, perhaps intentionally; modern English speakers do not expect the indirect object him in references to building something. The 1908 RLDS edition restored the him, probably by reference to 𝓟. The critical text will, of course, maintain the original him (the reading in both 𝓞 and 𝓟 as well as in all the early editions).
The typesetter for the 1874 RLDS edition omitted a number of minor words in this part of the text. Besides the him here in verse 5, the 1874 typesetter skipped also in verse 6 and again twice in verses 14–15. He also replaced more with other in verse 7. In each case, the 1908 RLDS edition restored the correct reading to the RLDS text.
Summary: Maintain the original reflexive pronoun him in Alma 63:5 (“and built him an exceeding large ship”).