Any employer or person aggrieved by any decision of fact or law by the director with reference to its or his or her status as an employer or as to whether services performed for it or him or her constitutes employment, or as to any other matter for which an appeal is not otherwise provided in chapters 42 — 44 of this title, may, within fifteen (15) days after notice of that decision has been mailed or otherwise delivered to it or him or her, appeal to the board of review, in writing, stating the grounds upon which that appeal is taken. Unless an appeal is duly filed within the time limit, the decision of the director shall be final. If any appeal is duly filed, the board of review shall then set a time and place to give the appellant an opportunity to show cause as to why the decision of the director should be changed. Following that hearing, the board of review shall, as promptly as possible, notify the appellant and the director of its decision on the appeal. That decision shall become final unless the appellant or the director files an appeal to the courts in accordance with the provisions of § 28-44-51 — § 28-44-55.