> so "alphabetical" order is a meaningless concept
Japanese does have its alphabetical order. It's called gojyuon-jyun (or aiueo-jyun) [1], and most commonly used dictionaries use this order [2].
[1] https://ja.wikipedia.org/wiki/%E4%BA%94%E5%8D%81%E9%9F%B3%E9...
[2] http://octoba.jp/wp-content/uploads/2015/11/jp.ne_.biglobe.s...