By non-Islamic, I mean a country that is not ruled according to Shariah. Not necessarily non-Muslim-majority. For example, my country, Bangladesh, is a Muslim-majority country, but not a Islamic country.
And by rules, of course I mean those rules which do not contradict Shariah. I am sure if a rule contradict shariah, it cannot be obeyed by a Muslim.
I believe most countries have an age restriction for marriage. Bangladesh has 18 years for women and 21 years for men. Now, I have seen many people give their daughter to marriage before 18. Perhaps because it is encouraged by the Prophet (S).
Now, Is it farz for a Muslim to obey such a rule? Or it depends on situation and type of the rule.