Corn is just a cheap grain. It is not bad and provides some calories but does not provide a lot of nutritional benefits. It is very cheap so dog food companies, which of course want to produce their food as cheaply as possible, will add it to provide a nutrient at a low cost.
Coconut oil will help a dog with a yeast infection because the vitamin E and other antioxidants will help protect against damage by free radicals. Free radicals can cause some of the damage to a yeast infected skin, like the wrinkles.
Coconut oil also acts as a moisturizer, and allow the skin to heal, aiding in closing the small scratches from the itching associated with yeast infection.
By itself, the coconut oil is not adequate. You must first remove the bulk of the yeast with shampooing and then kill the others with apple cider vinegar.