You are right, in the first sentence “l'ordre des choses” expresses a natural consequence. “Ordre” has temporal and causative implications. Wiktionary provides the following definition:
Ce qui arrive, ce qui se passe, sans qu’il soit possible de le discuter, de le refuser.
Quite surprisingly, in the second sentence it's used with a much more literal meaning. If all things were ranked according to how precious they are to us, he would come before you (by far). “Ordre” is to be understood as a comparison order, but using “ordre des choses” for a universal, absolute scale of importance in this way sounds very unusual1 and quite literary.
1. Apparently it was chosen for lack of a better translation that fits the format of subtitles.