Dairy-free substitute for milk when marinating chicken
Milk has been used in marinades for a long time, and it does work. It is thought that it is the calcium in the milk that activates enzymes in the chicken rather than enzymes in the milk tenderizing the chicken, see this article for the science. This means you can use soy, rice, or any milk substitute, but you'll get the best result from the one with the most calcium. This article lists the mg of calcium per 1 US cup (235ml) of cow's milk and substitutes:


Cow's milk: 300mg
Rice milk: 283mg
Coconut milk: 41mg
Soy milk: 19mg


So it looks like Rice milk is the best substitute from a tenderizing perspective.

There are other ways of tenderizing chicken, pineapple for example does a great job, however if you want authentic middle eastern milk substitutes are the way to go.