I don't think there is a specific type of magic. Robert Graves I think just decided on Aboriginal shout to make his short story a little more exotic. The stones in the story do represent the souls of everyone in the village.
It's a fascinating and wonderful story well worth reading. I scarcely believe it was written almost a century ago, as the plot, storyline and style of writing feels modern.
I don't know exactly why Graves wrote the story, but he was married at the time while carrying on quite a public affair with another woman (the poet Laura Riding) while at Oxford; an affair that eventually near the end of the 1920s led to him being accused of trying to murder his wife, his mistress attempting suicide and him fleeing with his mistress and his children to Spain (which had no extradition treaty with England).
Bearing all this in mind, one can perhaps see that the story is not so much about magic as a reflection on the complicated and emotionally intense relationships Graves was involved in at the time.
That said, he was also very interested in very ancient matriarchal history and mythology which he explored in his seminal book, The White Goddess and, to a lesser extent, The Greek Myths. So it's highly possible that the magic he describes in this story was based on 'real' magic.
Thanks for the comment. If I get the chance, I'll have to read the story sometime.