The authors are proposing a taxonomic reclassification to simplify things.
My understanding is that they suggest doing away with heidelbergensis. That makes sense, since the European heidelbergensis and the African heidelbergensis share the same time period, but there are significant differences. As the authors point out, the European fossils currently called heidelbergensis have key Neanderthal characteristics. They seem to fit an “early Neanderthal” better than a counterpart to the African examples of heidelbergensis. The authors of the paper thus propose combining African heidelbergensis and rhodesiensis as H. bodoensis. That moves European heidelbergensis out of the sapiens lineage as an MRCA.
Their reading of the evidence makes sense to me, but it doesn’t matter unless others adopt the terminology. I suspect scientists will agree to a new nomenclature for the African fossils, whether bodoensis or something else, but heidelbergensis will probably stick to the European branch. We’ll see.