That passage in the Book of Mormon is talking about one particular group of people at one specific point in time. The people were all Israelites (Nephite vs. Lamanites), with the possible exception that they may have intermarried with any other people that may have lived there. My own opinion is that the darker skin did come from intermarriage with others, and was symbolic of them forgetting the covenants the Lord had made with Israel. At any rate, it has absolutely nothing to do with people of African descent. Blacks in that context simply do not enter into the Book of Mormon at all. And that passage never even mentions Cain or Cain's curse.
That being said, there are certainly 19th and early 20th century LDS who did associate being black with the curse of Cain. As did many other nonLDS individuals of that time period. But as far as I know, they never used that passage from the Book of Mormon to justify it (there was another passage from the Book of Abraham that was used, if I recall correctly).