Tabby just means the striped pattern. It is not a breed or a color. There are different types of tabby patterns, like mackeral tabby and different colors like the brown (yours) silver or red etc.
About his dull fur, I would make sure he is on the correct food. Most coat problems are caused by the diet. Not all cats will have the same amount of shine in their fur, but you may be able to bring it up with a different food. But another thing to consider is his size. If he is a big cat he may have difficulty in cleaning certain areas like his back and that could aid in his appearing dull. If this is the case a little EXTRA brushing and/or a good bath may help.