Milkshake translates as milkshake, which means "milk", and shake means "past". Yesterday in Cantonese is Rusheng, pronounced as /sik 1/, so the word milkshake should be translated by Cantonese people, probably from Hong Kong first.

The so-called "Mi Xi" should probably be translated into rice milkshake or rice protein milkshake.

Rice shake is similar to what we call rice paste. It's what is cooked after broken rice.

Rice protein milkshake is a kind of protein separated from rice and purple rice, which is usually sold in liquid or powder form. The main consumers are vegans, as a substitute for whey protein milkshake/powder. This is because vegans refuse to eat dairy products, so rice products are a good substitute.