In Neolithic and early Bronze Age China, dogs were one of the more common domestic animals. The pig was much more common, but depending on when and where, the dog could be the 2nd or 3rd most common behind the pig, judging by counts of bones. Notably, the dog and the pig are the earliest domesticated animals in China, and elsewhere in Asia, the dog was first.
Were these working dogs? Some - and perhaps most - certainly were. A major use of dogs was hunting, and they were also used as guard animals and for herding. As populations grew, and hunting became less important as a source of food, hunting dogs declined in importance. Where herding was an important occupation (e.g., Tibet, if you consider Tibet to be part of East Asia, and Mongolia (in modern times, every herding family in Mongolia typically kept 1-3 guard dogs), guard/herding dogs were common. These dogs were often very large, in order to be able to deter wolves.
Dogs were also used for rodent control.
Other than as pets (a non-working role that became more important over time), non-working roles included sacrifice and a source of food.
References:
Modern guard dogs in Mongolia: N. Odontsetseg, D. Uuganbayar, Sh. Tserendorj & Z. Adiyasuren, "Animal and human rabies in Mongolia", Rev. sci. tech. Off. int. Epiz., 2009, 28 (3), 995-1003
Marco Polo on dogs in Tibet:
They have the very largest hairy mastiff dogs in the world, which are as large as asses and are very good at catching all sorts of wild beasts
(and there are many more descriptions of dogs and their use in hunting in his Travels).
On the early history of dogs in East Asia (and SE Asia and the Pacific): Greig, Karen, Richard Walter, and Elizabeth A. Matisoo-Smith. "Dogs and people in Southeast Asia and the Pacific." The Routledge Handbook of Bioarchaeology in Southeast Asia and the Pacific Islands (2016): 462-482.
Dogs in China:
E. N. Anderson, Food and Environment in Early and Medieval China, University of Pennsylvania Press, 2014
Dong, Yu et al. “Shifting diets and the rise of male-biased inequality on the Central Plains of China during Eastern Zhou” Proceedings of the National Academy of Sciences of the United States of America vol. 114,5 (2017): 932-937.
Han Dynasty dog with a collar/harness suggesting a working animal: https://i.pinimg.com/originals/8d/b5/79/8db579837c41ab6dd4cdf3d821d52645.jpg
... and another: https://i.pinimg.com/236x/da/70/c8/da70c8f4164e9512ed0d5d44ff4a527c--chinese-art-statues.jpg (the collar/harness with a chest strap and a ring on the back is common).
Qubilai Khan hunting with a dog: https://commons.wikimedia.org/wiki/File:KhubilaiOnTheHunt.jpg
