We apparently have a primitive error here. The earliest extant reading (in 𝓟 and the 1830 edition) read “the people of the king of Jacob”, so quite likely 𝓞 read the same. What the text seems to be saying is that the city Jacob-Ugath was inhabited by the people of king Jacob. This, in fact, is how the editors for the 1920 LDS edition interpreted this passage; they therefore omitted the of. Since the use of the definite article the before king Jacob sounded strange, they removed the definite article the as well. This editing is consistent with usage elsewhere in the text, with eight examples of “the people of king X”:
But as discussed under Mosiah 19:15, the original text had at least nine instances of “the king X”, where X is a personal name, such as “the king Noah” originally in Mosiah 19:15. Most instances of this usage have been retained in the current text, but punctuation has been used to treat the name as an appositive. So “the people of the king Jacob” is possible. Thus here in 3 Nephi 9:9 the critical text will emend the earliest reading to “the people of the king Jacob”, a minimal emendation that can be supported by usage elsewhere in the text.
This emendation assumes that during the dictation of the text an extra of was accidentally inserted between king and Jacob, perhaps because after the king one expects an of, given that “the king Jacob” is not standard English. One well-known phrase where a secondary of was apparently added during the early transmission of the text is “the Son / the Only Begotten of the Father”, found in Alma 5:48 and Alma 13:9. In both these instances, the earliest textual source (the printer’s manuscript) reads “the Son of the Only Begotten of the Father”. For discussion of that case of an extra of, see under Alma 5:48.
David Calabro (personal communication) suggests that the earliest reading here in 3 Nephi 9:9 is actually correct if one interprets the phrase “the king of Jacob” as a reference to the king of the city of Jacob. That city is listed in the previous verse: “and behold the city of Gadiandi and the city of Gadiomnah and the city of Jacob and the city of Gimgimno / all these have I caused to be sunk”. The previous reference to this king Jacob (in 3 Nephi 7:9–13) suggests that he could have founded a city of Jacob before he fled north to found another city, the city of Jacob-Ugath. Thus here in 3 Nephi 9:9 this king Jacob could be referred to as “the king of Jacob”. One problem with this proposal, however, is that the phrase “the people of the king of Jacob” seems quite unnecessary as a circumlocution for “the people of (the) king Jacob”. There are no other examples of such usage elsewhere in the text; as noted above, there are eight references to “the people of king X” (where X is a king’s name) but none to “the people of the king of Y” (where Y is the name of a city or land). And although king Jacob could very well have been the founder of the city of Jacob, having fled north to found the city Jacob-Ugath, he was probably no longer referred to as the king of Jacob.
Summary: Emend 3 Nephi 9:9 by removing the unnecessary of in the earliest reading, “the people of the king of Jacob”, giving “the people of the king Jacob”; there is considerable evidence for the phraseology “the king X” in the original (and current) text of the Book of Mormon; the 1920 LDS edition removed this of from 3 Nephi 9:9 but in addition removed the unusual the before king, giving “the people of king Jacob”.