Yes, it is spiritual/eccesiastical. In civil matters, during the time of Christendom, it was considered indirect by virtue of the organic unity between the Church and society in general. Temporal rulers were baptized subjects of the Church and the Pope shared with them the common care for the good of the baptized people of Christendom. By custom, the Pope would approve of new rulers in virtue of their good for those people and could intervene in extraordinary circumstances to even remove rulers (who were baptized members of the Church) where the salvation of the souls of his other subjects required it. But again, this required that organic unity of Church and society found in Christendom.
Some interpreted Boniface VIII’s Unam Sanctam as an attempt to assert a a more direct authority over civil rulers (particularly the French king), but Boniface denied it and that interpretation was formally ruled out by his successor, Clement V, in the brief Meruit.
Sixtus V privately held the opinion of a more direct power in theory. St. Robert Bellarmine opposed him on this point, earning the displeasure of the Pope, but Sixtus ultimately never pushed it anywhere and subsequent Popes approved St. Robert’s writings on the subject.
