وَأَوْلَى النَّاسِ بِالصَّلَاةِ عَلَيْهِ: السُّلْطَانُ إِنْ حَضَرَ.
Translation: The person with first priority to lead is the ruler, if present.
Awlā al-nās means the person with the stronger entitlement. The text gives the ruler priority within the legal-administrative context in which it was written.
This is a rule about precedence for leading the prayer; it does not change the four-takbir structure. Present-day practical leadership arrangements require their own context.