Should I describe automata before describing grammar?
In mathematics, the only thing that you absolutely must do is prove every theorem. Everything else is optional. In this case, you are asking whether every grammar formalism must be accompanied with a corresponding machine model. There is no such requirement, simply because not all grammar formalisms have a corresponding machine model which is natural. It is just a "nice to have" feature. More generally, the definition of a new class of languages is more convincing if the class can be defined in many seemingly different ways.

Another thing which you don't have to do but is "nice to have" is discussing closure properties of your class of languages, discussing the complexity of the classical decision problems for your class, and relating your class to other classes of languages. This is how people have studied language classes in the past, and so you would be expected to do it.