The subject pronoun they refers, of course, to the preceding many. Although such usage is redundant, it is quite frequent in the original text (see, for instance, the nearby discussion under Alma 43:36). In his editing for the 1837 edition, Joseph Smith not only removed the redundant they but added the relative pronoun that, giving “there were many … that were struck with fear”. The critical text will restore the original reading here since this kind of redundancy is found in the original text.
Summary: Restore in Alma 44:15 the original redundant subject they and remove the extra relative pronoun that (thus “there were many—when they heard these words and saw the scalp which was upon the sword—they were struck with fear”).