If any of the actual developers of this code choose to respond, they probably know better. But if-I-understand-correctly, the sparse incidence matrix shows how the new simplified state variables depend on the original state variables. So in the example above ω(t) would depend on 3 variables of the pre-simplified formulation. And the same applies to the other new variables.

The incidence matrix a structural representation of which variables occur in which equations. The rows are the equations of the system, the columns are the variables.