What are the signs (if any) in DOS plots that tell us whether we have a big or small crystal-field splitting energy, or spin-splitting energy? I already asked and got an answer to: What do we mean by spin-splitting energy?
I'm going to reproduce the part of my answer from the linked question that relates to the spin-splitting.
I don't believe the spin-splitting or field splitting can be read from the DOS. The way they are mentioned in the paper seems to suggest they are giving a qualitative explanation for seeing all the compounds in high spin configurations. The spectrochemical series gives an ordering of ligands based on how much field splitting they should cause. Since S is known to be a weak-field ligand, it makes sense that the spin splitting energy would be larger than the field splitting, leading to high spin configurations.
As for the crystal-field splitting, perhaps not from the DOS on its own, but the PDOS could help you identify the gap in energy between states formed from different types of d-orbitals.