My experience is limited to primarily coastal blacktail where sage and acorns are present so may not be applicable to other areas but here is what I try to do after the game is down.
First get it skinned ASAP. Hang it until it cools, usually overnight. I take mine to a local processor and they usually hang it for 2-3 weeks. I have been told that hanging deer does not make a difference as they don't have the same enzymes as beef but this works for me.
When ready to cook, make sure all fat and any meat exposed during the hanging process is cut off. You want only lean red meat, no grey or browned edges. I usually BBQ and marinade in balsamic vinegar, a little olive oil and garlic at least 4 hours but up to a day or so.
BBQ on a hot fire very quickly 3-4min per side for a 1 inch steak. It has to be rare, if it isn't, it will be tough and dry.
This works with our local deer and it still tastes like deer but the balsamic gives it a sweet flavor and there is no gamey taste whatsoever.
AS far as meat in Africa, my experience has been that it is cooked with all kinds of sauces and curry and it is more about the cook than the meat.
