Under 1 Nephi 8:20, I identified this passage in 2 Nephi 31:9 along with another one in 2 Nephi 33:9 for which either strait ‘narrow’ or straight ‘not crooked’ would work. The parallel language between 2 Nephi 33:9 and Matthew 7:13–14 (both refer to the way or path as “leading to life”) especially argues for the use of strait in 2 Nephi 33:9. There is, however, additional evidence in this chapter to suggest that here in 2 Nephi 31:9 this path “leads to life”:
The use of the demonstrative this refers the reader back to the earlier mentioned path in verse 9. And there is one more nearby verse that refers to this path:
In other words, 2 Nephi 31 links verses 18 and 19 to verse 9. This connection provides strong evidence that together 2 Nephi 31:9 and 2 Nephi 31:18 refer to the language of Matthew 7:13–14, just as 2 Nephi 33:9 does.
One could further argue that the use of strait in verse 9 implies that verses 18 and 19 should read “this strait and narrow path”—that is, redundantly. And correspondingly, the two other uses of “straight and narrow” in the Book of Mormon text (in 1 Nephi 8:20 and Helaman 3:29) should therefore read “strait and narrow”. This linkage may explain why the editors for the 1981 LDS edition decided to change all four instances of “straight and narrow” to “strait and narrow”. For further discussion of this issue, see 1 Nephi 8:20.
Summary: Evidence from 2 Nephi 31:18 argues that the text in 2 Nephi 31:9 refers to Matthew 7:13–14; thus 2 Nephi 31:9 should probably read “the straitness of the path” even though 2 Nephi 31:18 reads “this straight and narrow path”.