from a quick glance at the text i think he means legally institutionalized private property or equivalent.

but he as an anthropologist has argued in other venues to revise historical origins of various concepts like currency and debt based on available evidence rather than academic myth.

which is an earliest known origins argument based on available archaeological evidence rather than true earliest origins or mythologized origins for propagandized explainability. Of course this isnt relevant to your dog point, but just to contextualize a reoccurring theme of Graeber.