Buttermilk

I meant “do” instead of “ drive.”

From experience, if a cake is on the crumbly side, add more eggs. I see recipe asks for two, use three instead.
As for making it more moist, replace some of the butter with oil using formula butter = 80% oil 20% milk. This formula has never failed me. For this particular chocolate cake which asks for 9 tbsp butter, i would do 4 tbsp butter, 4 tbsp vegetable oil (80% of 5) and 1 additional tbsp milk (20% of 5). As for replacing milk with buttermilk, the later does make a cake more tender but you may have to add more baking soda. I would just drive my egg and oil suggestion.