In his editing for the 1837 edition, Joseph Smith deleted the redundant these in this complex sentence. Nonetheless, restating a form of the subject helps the reader process the sentence. If there had been no parenthetical explanation (that is, if the phrase “or all those that have kept the commandments of God” had been lacking), the reader would indeed expect the these to be missing: “and all those that have believed in their words shall come forth in the first resurrection”. Restating the subject after a parenthetical intervention occurs fairly often in the original Book of Mormon text. For further discussion of this kind of redundancy, see under 2 Nephi 10:3; for an extensive list of examples, see subject repetition in volume 3.
Summary: Restore the redundancy of the original text in Mosiah 15:22: “and all those that have believed in their words … these shall come forth in the first resurrection”; such usage can be found elsewhere in the original text.