The Nuggies were a species of timid mole-like sentient beings who had once been the dominant species of the Tin Isle. Their economy was sustained by mining tin and trading it with the Centaurs among others. One day mans appeared on the Tin Isle and the Nuggies went nearly extinct.
When tin shipments stopped arriving in the Centaurs' homeland, the Centaurs sent an expedition led by Cheiron to attempt to reestablish contact with the Nuggies. On hearing of their fate from the survivor Bucca, and on making contact with the mans, Cheiron demanded that the mans stop their genocide against the few surviving Nuggies as a condition of the trade agreement which he negotiated with Geraint. Geraint, confused, informed Cheiron that the mans were not engaged in any violent activities against the Nuggies and never had been. Cheiron asked why they had been brought to the brink of extinction, and Geraint informed him quite matter-of-factly that ever since the mans had appeared on the Tin Isle, the Nuggies had been dying of shame.
Though centaurs were much stronger-willed than Nuggies, Cheiron was able to understand how the presence of mans might instill such shame in all other creatures.
Spriggans and piskies were related species, which declined noticeably at the same time as the Nuggies.
While all the other mythological species in "The Horse of Bronze" are well known from classical literature, the name Nuggies appears to be Harry Turtledove's own invention. Spriggans and piskies are known from British folklore, however.