Heat bacon fat in a 5-quart Dutch oven over medium heat. Add onion and cook until tender, about 5 minutes. Add venison and brown well, about 10 minutes.
Brown beef in a separate skillet over medium heat, 7 to 10 minutes; add to Dutch oven with venison. Brown pork in the skillet over medium heat, 10 to 15 minutes; add to Dutch oven with meat mixture. Add chili powder, cayenne pepper, garlic, and cumin. Cook over medium heat until flavors have combined, stirring occasionally, about 30 minutes.
Stir tomato sauce, water, tomato paste, paprika, parsley, salt, and oregano into the meat mixture in the Dutch oven. Bring to a boil. Reduce heat to a simmer and cook for about 1 hour. Stir occasionally and add water as needed.
Mix masa harina into the meat mixture in the Dutch oven; cook until thickened, at least 30 minutes. Add more water as needed.
