Most cuisines have learned to cook food from what they have around them in nature for 1000s of years. This was animal products and whatever vegetates they could get their hands on. Over time popular dishes were the ones that tasted great with that they could could source from their region. So meat free dishes are not really a problem from a chiefs point of view as recipes from earlier times would had access to dairy products, milk, cream, cheese etc to be used in dishes.
Veganism on the other hand hasn't had as much widespread appeal until modern times, although single item vegan recipes do make up parts of cusine its not easy to say create a meat pie using vegan products. The meat can be replaced, but the problem is that fats from animals have different properties, one. being viscous enough at room temp, than plant fats them unsuitable for cooking, another being that certain favours (herb) are imparted on fat, another being that animal fat, dairy are cheaper.
Some of this is somewhat overcome with the use of palm oil which have enough saturated fat that can replace animal sourced fats and is cheap enough to be used. However, this has its own problems.
So basically, vegan cuisine is somewhat lagging behind non-vegan cuisine.