The prior entry may be found here: https://memoirandremains.wordpress.com/2013/07/24/lex-rex-3-do-we-need-a-king/
To understand this question, we must first understand Rutherford’s doctrine of divine action, which would currently go by the title “compatibilism” or as Feinberg has it “soft determinism”.  In one sense all actions the result of God’s determination. However, in acting through human beings, God does not make a human being do something they do not desire to do. Rather, the determination of God and decision of the human being are compatible (please see the entire discussion by Feinberg to understand the nuances).
The concept is important to Rutherford’s argument, because he is considering whether a man becomes king because God has made him King or because the people have chosen the king. Romans 13:1 states that all authorities exist because God has appointed them. Thus, some would argue that I am king because God made me king: Therefore, everything I do is right (because God has willed it).
Rutherford nuances the argument by noting that with very possible exceptions (such as David being anointed as king by Samuel), no King was chosen by immediate act of God (there is no prophetic announcement that Mr. X will be king, in most instances). He gives the example of a biblical prophet. Jeremiah is a prophet because God made him a prophet. The fact that no one wants him to be a prophet does not change anything. Yet even David at some point must reckon with the willingness of the people that he be King:
The prophets were immediately called of God to be prophets, whether the people consented that they should be prophets or not; therefore God immediately and only sent the prophets, not the people; but though God extraordinarily designed some men to be kings, and anointed them by his prophets, yet were they never actually installed kings till the people made them kings.
God has decided that David will be king. God gives a prophetic word that David will be king. God also works through the people of Israel to make David king. But unless we are going to reduce Providence to fate and human beings to robots, we must take seriously the human interaction.
If they mean by the people’s choosing nothing but the people’s approbative consent, posterior to God’s act of creating a king, let them show us an act of God making Kings, and establishing royal power in this family lather than m that family, which is prior to the people’s consent,—distinct from the people’s consent I believe there is none at all.
Why then kings at all? Rutherford explains that to defend ourselves from violence (the common defense), it may make sense to have a ruler who can wield an army. Thus, the people are choosing someone to protect them. Moreover, people choose the local magistrates who rule over them; how much different is it than choosing a king?
And how then a king?
If all men be born, as concerning civil power, alike,—for no man cometh out of the womb with a diadem on his head or a sceptre in his hand, and yet men united in a society may give crown and sceptre to this man and not to that man,—then this power was in this united society, but it was not in them formally, for they should then all have been one king, and so both above and superior, and below and inferior to themselves, which we cannot say; therefore this power must have been virtually in them, because neither man nor community of men can give that which they neither have formally nor virtually in them.
And so he concludes that is the choice of the people that results in the king (even though such choice accords with God’s decision):
I think royalists cannot deny but a people ruled by aristocratic magistrates may elect a king, and a king so elected is formally made a lawful king by the people’s election; for of six willing and gifted to reign, what maketh one a king and not the other five? Certainly by God’s disposing the people to choose this man, and not another man. It cannot be said but God giveth the kingly power immediately; and by him kings reign, that is true. The office is immediately from God, but the question now is, What is that which formally applieth the office and royal power to this person rather than to the other five as meet? Nothing can here be dreamed of but God’s inclining the hearts of the states to choose this man and not that man.
This argument then opens the further consideration (not here addressed by Rutherford): If the consent of the governed is what makes a king (and such consent comes from God); then the retraction of consent must also derive from God.
Rutherford then also turns God’s will in appointment of a king against a king. Since the office is a gift of God (in the ultimate sense), the king must acknowledge his rule as not originating in his own goodness and fitness but rather in God’s gift:
But there is no title on earth now to tie crowns to families, to persons, but only the suffrages of the people: for, 1st, Conquest without the consent of the people is but royal robbery, as we shall see. 2d, There is no prophetical and immediate calling to kingdoms now. 3d, The Lord’s giving of regal parts is somewhat; but I hope royalists will not deny but a child, young in years and judgment, may be a lawful king. 4th, Mr Maxwell’s appointing of the kingly office doth no more make one man a lawful king than another; for this were a wide consequence. God hath appointed that kings should be; therefore John à Stiles is a king; yea, therefore David is a king. It followeth not. Therefore it remaineth only that the suffrages of the people of God is that just title and divine calling that kings have now to their crowns. I presuppose they have gifts to govern from God.
 “Soft determinists agree that everything happens is causally determined, but they also believe that some actions are free….Compatibilists contend that there are free actions and those actions, though casually determined, are free because they are done in accord with the agent’s wishes” (Feinberg, No One Like Him, 635 & 637).