Mdd,
1. Rambam says (Hilchot Melachim 1,7) that only David’s kosher descendants can be king. Does that mean that the kings of Israel were not kings according to Rambam (see Sanhedrin 20b Tosafot d”h melech)? What about Menashe ben Chizkiahu? Rambam also says (ibid, Hlalacha 8) that if a navi appoints someone from a different shevet to be king and he keeps the Torah he is considered the king. Does that mean that the Hashmonaim and the Herodian rulers were not kings? If not, how do you define their government?
2. Abarbanel, the Netziv, Rav Kook and Rav Chaim David HaLevi (“Shilton al pi HaTorah v’haDemokratia”, “Shana b’Shana”, 5758, p.205-213) apparently interpret it differently. I only suggested that according to them the mitzva to appoint a king means a central government and not necessarily a monarch. If you wnat to disagree you can cite opposing sources. However, let us not be neo-Karaites.