These verses provide the vision’s definition of the newly arriving Gentiles. They are part of the explanation of the war between the church of the Devil and church of Jehovah, and they are therefore defined in such a way that their ascendance over the remnants of the Lamanites will be the logical fulfillment of prophecy. Thus, they are described as the complete opposite of the Lamanites who are already in this world that the Gentiles are just entering.
Remember that in the previous chapter (1 Nephi 12: 23), the Lamanites were described as “a dark, and loathsome, and a filthy people, full of idleness and all manner of abominations.” The Gentiles are clearly opposites: “white, and exceedingly fair and beautiful, like unto my people before they were slain.” The description of the Gentiles intentionally reverses the description of the Lamanites.
It is also important that Nephi indicate that the Gentiles “did humble themselves before the Lord.” These Gentiles will enter a land to which a promise has been attached. There will be prosperity, but only upon conditions of righteousness. Nephi’s vision sets the Gentiles up as the inheritors of the promise of the land. They are righteous. Therefore, they prosper. Specifically, they will prosper over the Lamanites who have dwindled in unbelief.
The power of the promise of the land is reasserted with these newly dominant Gentiles. Now that they are in the land of promise, and now that they inherit that promise—still upon conditions of righteousness—they are also dominant above those of their former brethren who fight against them.