As noted in the discussion of the same phraseology nearby in verse 18 (“and then are ye in this straight and narrow path”), the demonstrative this ultimately refers the reader back to the discussion in verse 9. The this is clearly intended in both verses 18 and 19. Here in verse 19, the 1858 Wright edition replaced the this with the, but the instance of this in verse 18 was left unchanged, thus showing that the 1858 change here in verse 19 was probably a typo. As also discussed under 1 Nephi 8:20 and 2 Nephi 31:18, the conjoined adjective here is straight, not strait.
Summary: Maintain the demonstrative this in 2 Nephi 31:19 as well as the nonredundant conjuncts straight and narrow.