The Rule of Law is a fundamental idea in governing. It concerns itself with the set of rules, codes and laws that a group adheres to uniformly i.e all members of this group adhere to it. However all rules of law are universal, or in other words all rules of law are not Christian in that they believe that there is one law for all of man. As Atavisionary describes, the ancestral heritage of this egalitarian view of life comes from Martin Luther during the age of the Reformation.
The Rule of Law has to do with sovereignty, in that the sovereign decides the rule and the exception.  The sovereign can only be considered sovereign when it is backed up by an institution. What would define this institution and how would it function?
Well the first question the institution must ask itself is – how does it fashion it’s rule of law? For this it would have to begin to understand what is the law itself and where does it come from – in other words does man make the law or is the law natural or self-evident. If this resembles the Euthyphro Dilemma, it is not a coincidence. Fact is there is no natural law 
There are no natural rights only natural tyrannies.
This would be surprising only if one has not been playing close attention to the farce that is the United Nations. For one thing members of the OIC (of which TSP is a member state), reject wholesale the Universal Declaration of Human Rights but affirm and endorse the Cairo Declaration of Human Rights In Islam. This is because the rights of human beings are metaphysical assumptions and are constructed by the sovereign. And how does one enforce sovereignty? By violence. 
It follows that every right you believe you have, you do only because the sovereign you are ruled by allows you to have that right. So what sort of a sovereign will protect your rights the most? In other words, which form of government has the most incentive to continue to allow you to exercise the rights you have?
Justice can only be dealt from a position of power.
Democracy, simply under game theory is unstable as has been discussed earlier. Democracies favour policies which garner it the most votes, and every actor in a democratic system is interested in maximizing his odds at re-election not necessarily at maximizing the national interest. Lee Kwan Yew was very famously anti-democracy and look where Singapore is today.
There are alternative forms of government, one is formalism where Moldbug
takes Libertarianism to an extreme. discusses some consequences of power and how power structures would operate in neo-reaction. Suffice to say such a form of government seems ludicrous to the lay Hindu, since he is aware that violence is universal and will never be done away with as long as conflicting groups exist. Another is oligarchy where privileged well educated nobles administer the nation. But why not a Monarchy, with a God King administering his kingdom in the name of our illustrious ancestors.
A case for monarchy is actually quite obvious given that Monarchs are sovereign to the fullest degree.
- They are unconcerned with re-election and their absolute control of the military allows them to stifle dissent. If there is a worry that the military may turn on you, then this is foolish since it’s likelihood under democracy is both non-zero and the basis for America’s 2nd Amendment. Ibn Battuta notes that the the Lower Caste populace in India resisted the Mughals by firing their matchlocks and their women helped them so Hindus have historically had the right to bear arms.
- They are religious figure heads who represent the entirety of the country. They are well educated in economics, polity, literature and law and are trained from birth to dispense one singular duty – to rule over their people with fairness and kindness.
I leave you with an explanation of the actions of our Lord Rama in the Uttara Kanda of the Ramayana. Cohabiting with a male in Treta Yuga beyond a certain period was considered unlawful. Man and wife were supposed to separate, the man would support the wife but they could not be together in the true sense of a marriage. When Lord Rama meets Sita Devi she suggests that she undergo the Agni Pariksha  to prove her chastity in her husbands absence much to the distress of our Lord. After her succeeding the test of fire, she and our god return to Ayodhya and the public was subdued for a time.
However Sita’s subsequent pregnancy led to obvious insinuations and public pressure mounted on Rama to uphold the law. Since he was the king, and the kingdom was his property his wife had to be banished beyond the extent of his kingship. Our Lord was devastated and remained married to her in name as is evident by his undertaking Yagnas post her departure which can only be performed by a member of the grhasthashram (the stage of the householder). He performed it with a gold idol of her in his lap – gold signifying the value and the idol representative of her.
Through the sage Valmiki he becomes aware of the birth of his now grown up sons, and he takes them back and asks his divine wife to rejoin him. She refuses and is swallowed up by Bhumidevi. Distraught, he crowns his son, leaves with a few close friends, and walks into the river Sarayu, drowning himself.
Can one attain a higher degree of nobility? Jai Shri Rama!
 For a fantastic description of what it would entail to be truly sovereign I recommend Social Matter. Hindus would do well to understand just how low they score on any valid measure of sovereignty.
 Sri Krishna speaks –
Everything has its proper utility, and a man who is situated in complete knowledge knows how and where to apply a thing for its proper utility. Similarly, violence also has its utility, and how to apply violence rests with the person in knowledge. Although the justice of the peace awards capital punishment to a person condemned for murder, the justice of the peace cannot be blamed, because he orders violence to another person according to the codes of justice. In Manu-saṁhitā, the lawbook for mankind, it is supported that a murderer should be condemned to death so that in his next life he will not have to suffer for the great sin he has committed. Therefore, the king’s punishment of hanging a murderer is actually beneficial. Similarly, when Kṛṣṇa orders fighting, it must be concluded that violence is for supreme justice, and thus Arjuna should follow the instruction, knowing well that such violence, committed in the act of fighting for Kṛṣṇa, is not violence at all because, at any rate, the man, or rather the soul, cannot be killed; so for the administration of justice, so-called violence is permitted. A surgical operation is not meant to kill the patient, but to cure him. Therefore the fighting to be executed by Arjuna at the instruction of Kṛṣṇa is with full knowledge, so there is no possibility of sinful reaction.
EDIT:  As the Acharya points out the Agni Pariksha is a later regional addition.