I imagine that SO6P did not go about hitting individuals with the DNA sword. I imagine that he plunged the sword into the Earth itself, and this indirectly affected people who met his criteria, and perhaps other non human creatures too. However it is quite possible/feasible that he used the sword on individual creatures too.
I would further postulate that once he had altered the DNA of beings on the planet, he then himself went on his pilgrimage teaching people how to use the chakra for their benefit, in a peaceful way. Unfortunately, his intentions were corrupted with people and their hatred and greed.
Or that's how I imagine the whole thing went down.
Note that Obito in his self visiualization, had one eye, and was half spiral Zetsu. What is implied is that Obito could have refused Madara's invitation, and left him dead, and returned to Konoha after Rin died. Then he and Kakashi together would have visted he grave. Paths not taken etc...