As explained earlier (see commentary on 2 Nephi 5:10), the Nephites lived the Law of Moses in the sense that they obeyed the endless ethical laws and abided by the myriad moral restrictions (Promised Messiah, p. 427).
They kept the Ten Commandments. They observed the law of animal sacrifice. But theirs was not a Levitical life-style; they had the higher priesthood and the everlasting gospel.
Their vision was more keen than that of their old-world kinsmen—they were able to recognize the person and powers and religion of Christ the Lord behind the ritual of the preparatory gospel.