Complex sentence: The Tainiste was chosen from among the heads of the "roydammna" or "righdamhna" (literally, those of "kingly material") or alternatively among all males of the sept in question, and elected by them in full assembly.
Split into simpler sentences: The Tainiste was chosen from among the heads of the "roydammna" or "righdamhna" (literally, those of "kingly material"). Or alternatively among all males of the sept in question, and elected by them in full assembly.