Can I use a non-dairy type buttermilk for this recipe? If so, how does one make non-dairy dairy buttermilk???

There is such a thing as vegan buttermilk- made using almond or soy milk- possibly others, and lemon juice. A quick web search will get you several dozen versions of the recipe. A I have no idea how well that would work for this particular recipe though. Buttermilk, the dairy sort, performs several tasks in the recipe, which vegan versions would not. No lactic acid, for starters, no milk sugars, and unknown amount of fats. Plus something like oat milk would most like curdle and thicken on being heated. If you can't tolerate dairy, it might be best to find a nice marinade based on something else, like sour orange juice.