Yes chicken sausage is a processed meat.
Any meats that are not fresh and are packaged including the chicken sausage and any other sausage is a processed meat.
Processed meat including chicken sausage is processed at a food plant where the add salt and other preservatives to the meat.
So since the chicken sausage has the addition of the salt and other ingredients and is packaged and then shipped out it is processed.
Meat is not processed if it's fresh such as if you kill a chicken yourself and then cook it to eat it.
Any store bought meat is a processed meat.
Turkey, duck, fish and poultry are all processed meats including pork and beef.