Law is the concern of all humanity…”Pray for the welfare of the state” (Avot 3:2), for it is the state that establishes law in the land: “The king by justice establishes the land” (Proverbs 29:2). And all of this is equally true of non-Jewish governments, for the descendants of Noah were also commanded concerning dinim. (Rav Avraham Koo, introduction to tractate Sanhedrin (1934) (see R. Moshe Tzvi Neriah, Tehumim, VII (1986), 275. )
The Noahide commandment of dinim establishes a point of commonality between the Jewish people and other nations on the most fundamental level of social existence.
…statutes based upon reason are incumbent upon the descendants of Noah. …The most important aspect of the commandment of dinim is… the very obligation of establishing the rule of law, of justice, of rationality, and of natural equity.
(Nahum Rakover: Law and the Noahides, The Library of Jewish Law, 1998, p. 112.)