Here in the 1902 and 1905 LDS missionary editions, the determiner this in the phase “the history of this people” was replaced (probably accidentally) by the. The change was apparently due to the influence of the phrase “the people of Nephi” that is found in the following relative clause (“which are called the people of Nephi”). The correct this was restored to the LDS text in the 1911 edition.
Summary: Maintain in Jacob 1:2 the original determiner this (“the history of this people”).