Why isn't the beef fat in my chili melting?
Not all the fat in beef (and generally, in any kind of meat) is the same. 

Any piece of meat will have a certain amount of marbling fat, which is intramuscular and is hard to remove, intermuscular fat and subcutaneous fat, which can be trimmed off. 

From your picture, it seems to me that the fat covering the outer layer of the beef chunks is gristle, which you can easily remove after having cooked your Chili. It is however hard to remove by increasing the temperature, as fat molecules are generally quite big and they are not soluble in aqueous solutions, which makes them kind of float on your sauce in an emulsion. 

From my experience as a cook, the best tip I can give you when it comes to Chili or stews is to choose a lean piece of beef, with as little as possible of visible marbling fat and before cooking, to remove as much of the visible fat as you can possibly do. Cooking it gently for four hours will make sure that the meat remains as tender as you can wish. :)