I am not an expert on this type of model but after reading their methods section a little more thoroughly, this is my sense:

I don't believe there is any case where a molecule in one voxel knows about molecules in other voxels. DNA and RNA is coarse grained where a 'molecule' might represent a specific sequence of interest rather than a full chain. Transcription and translation are modeled, essentially by saying if the neccessary ingredients are present in a voxel (DNA/RNA sequences, enzymes, raw materials, etc) there is some chance of forming mRNA or a protein as a function of the molecular concentrations present in the voxel. DNA and RNA reactions are treated with somewhat different equations than the rest of the molecules, I think to handle the coarse graining.