It's not sensible to call out non-alphabetic (by which I imagine you exclude all phonemic systems including abjads, syllabaries, etc all of which have full character order.

Even in Latin scripts, sorting order is language-specific and can even be domain specific (e.g. some languages sort phone books differently from dictionaries).

For "CJKV" systems there are ordering methods such as radicals and, as in European languages, ordering can depend on what you want to accomplish.