In the article cited by Simpson in creating the rough cladogram of Figure 3.1, _From algae to angiosperms-inferring the phylogeny of green plants (Viridiplantae) from 360 plastid genomes_ (Ruhfel et. al, 2014), the phylogeny of Viridplantae is inferred from a set of 78 genes.
Thus, the division of Viridiplantae into the two sister groups Chlorophyta and Streptophyta is inferred / supported by molecular evidence.