As regards the question of when ruling by other than what Allaah revealed is kufr asghar, which does not exclude a person from the ummah of Islam:
the answer is that this may be the case when a ruler or judge passes judgement according to other than what Allaah revealed out of disobedience or on a whim, or as a favour to someone, or because he was bribed, and so on, although he believes that it is obligatory to judge according to what Allaah has revealed, and that what he has done is a sinful and haraam deed.
As regards the one who is governed by a non-Islamic law, if he refers to it out of choice, then he is a kaafir whose kufr akbar means that he has left Islaam. But if he has no choice but to refer to this law, and does so reluctantly, then he is not a kaafir, because if he had been able to resort to sharee‘ah, he would have done so, and he believes that this non-Islamic law is false.
And Allaah knows best. May Allaah bless our Prophet Muhammad.