In the solution for the redox problem, the guy split up the equations in to two, but he also removed the S from the MN when he splited them up.
This redox reaction is not balanced, so in order to balance it, you need to split the reaction into two half reactions, an oxidation half and a reduction half, that is what this guy has done. The reduction half equation is MnO
4- ---> Mn
2+ and the oxidation half equation is S
2- S. Then you balance these two half reactions individually.
Some of the (non oxidised) sulphur remains with Mn in MnS (where S is in the -2 oxidation state) and some of the sulphur exists as elemental sulphur, where is it in the 0 oxidation state.