Found the same story from another source;
https://www.dailymail.co.uk/news/article-7952487/Communities-China-threaten-cull-residents-pets-coronavirus.html
The closest thing to sauce DM links to:
http://www.anshan.gov.cn/html/ASSZF/202001/0158035032853442.html
Google translation:
On January 29, Anshan City's headquarters for the prevention and control of major animal diseases issued an "Emergency Notice on Immediately Stopping Pet (Dog and Cat) Trading Activities". At the same time, Anshan Municipal Bureau of Agriculture and Rural Affairs issued the "Emergency Notice on Strengthening the Management of Poultry Pigeons and Poultry Pets".The notice requires that the city temporarily close the pet trading market, and the specific opening time is to be notified; the supervision department of the pet market location must stop accepting dog and cat quarantine declarations, and notify the local logistics company to suspend pet transportation; train stations, passenger stations, highways, etc. The department immediately suspended pet transportation; the public security department will strictly restrict dog walking in public places, strengthen the supervision of stray dogs and cats, and continue to implement compulsory rabies immunization; the agricultural comprehensive law enforcement department of the Municipal Agriculture and Rural Development Center will form an inspection team to increase the illegal transportation of pet dogs Cat's blow strength.At the same time, the city completely prohibits the listing and trading of live birds, and the domestic pigeons are restricted from flying. The free-range wild pigeons are responsible for the killing by the movement supervision department where they stay and live. Once the public finds pigeons and birds of unknown cause to die, they must immediately Report to your local veterinary department.
Could be true. Probably exaggerated/confused by journalist for the clicks. The Chinese know that this would be ineffective and would only lead to discontent.