Spatially heterogeneous means that the composition varies as a function of position within the material (varies "in space").
Chemically heterogeneous means that the chemical composition just varies in general. In this case, I assume they desire to emphasize that the composition varies among species of widely differing molecular weights—from large polymers down to small molecules.
So, it appears to me that "spatially and chemically heterogeneous" was used to emphasize that the chemical composition varies significantly, in particular as compared to prior assumptions; and that this compositional variability itself varies as a function of position within a given volume of the material.
In general, "spatially and chemically heterogeneous" would be rather a redundant term: a material can't really be spatially heterogeneous without also being chemically heterogeneous: if a substance is chemically pure, there is no possibility of any spatial distribution of compositional variations. So, I think the particular history of this material, which apparently had been assumed to consist only of polymeric material, is what led the authors to use the phrase.