TL;DR: According to Chinese official reports, China has essentially eliminated local transmission. This is consistent with reports from international news (reporting widespread tourism in China) and academia (a mathematical model of the Chinese lockdown; researchers having to test vaccines in other countries). Up-to-date coronavirus news in China is in Chinese, and the language barrier likely inhibits promptly updating the unofficial Worldometer website. Outbreaks like in Beijing and Xinjiang are widely reported so people get tested. (And if there were local transmission in China, the infected would simply tell people.)
Let's start here:
Worldometer's coronavirus tracker, based on data provided by each country's government...
Worldometer is not an official data repository (despite its popularity); it's was made by some guy (Andrey Alimetov) in the USA; more reliable sources are the ECDC and ArcGIS. Worldometer certainly doesn't have pinpoint accuracy; see e.g. Max Roser taking to Twitter to criticize its accuracy.
Further, it appears that the Chinese government is reporting some data that may not be included in Worldometer's statistics.
The Chinese government does not report to Andrey Alimetov so he can update his website. Instead, anonymous sources search the web and add it to Worldometer. There's likely a language barrier inhibiting updating Worldometer; they only seem to list English-language sources.
News from the 7-th October reports 53 consecutive days of no local transmission: 11 imported cases (of which 8 are asymptomatic). If we're not trusting such news, then we're talking about a major cover-up. This is impractical for multiple reasons, e.g.:
Modern China has hundreds of millions of people (Chinese and international) with constant Internet access and video cameras (obligatory XKCD comic). If infected people (and their family, friends, workmates, etc.) are not part of the cover-up, they'll blab on social media (e.g. warn people they have an infectious disease).
There's the contradiction between a cover-up and the not-covered-up breakouts in Beijing and Xinjiang. In fact, it needs to be all over the news so people get tested (I was in Beijing and I got tested).
There are reports from news outlets like CNN of widespread tourism in China (e.g. 1, 2, 3, 4), despite not being afraid to publish unflattering articles about China.
There are also relevant points in academia:
Researchers studying coronavirus treatments (e.g. vaccines) are struggling to find enough patients in China to conduct testing:
These trials usually require tens of thousands of participants, and with the outbreak in China largely under control, companies are having to test their vaccines elsewhere.
Cyranoski, China’s coronavirus vaccines are leaping ahead – but face challenges as virus wanes, Nature, July 2020.
There are mathematical models of the coronavirus outbreak and its containment in China:
The recent outbreak of coronavirus disease 2019 (COVID-19) in mainland China was characterized by a distinctive subexponential increase of confirmed cases during the early phase of the epidemic, contrasting with an initial exponential growth expected for an unconstrained outbreak. We show that this effect can be explained as a direct consequence of containment policies that effectively deplete the susceptible population.
Maier, Brockmann, Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China, Science, May 2020
...it seems unusual that a continental country with a sixth of the world population and with more borders than almost any other country, including with India and Russia, which have many cases, could completely eliminate the pandemic...
While China has many neighboring countries, all arrivals have mandatory testing and 2-week quarantine. (I've been told by friends this is at the traveler's expense; ~600 yuan per night, plus hotel meals.)
And I think it's fair to say that China is simply further ahead in the timeline: China's lockdown started in January, a few months before most other countries.
Update: My Chinese teacher brought my attention to a current outbreak in Qingdao. The most recent news (from 5 hours ago) is this where the Qingdao Municipal Health Commission report 3 newly discovered cases from yesterday, and discovered 9 cases among close contacts, and 0 cases among close contacts of close contacts. They also report testing 277968 people in hospitals (staff, patients, etc.), and thus far all have tested negative. CNN reports that "testing will now be rolled out citywide for the entire population of nine million".
The 3 cases identified in yesterday's news are described in detail. To give you an idea of how much detail is included: two of the sick are a 57-year-old man with the surname Shao and his wife a 53-year-old woman with the surname Jiang. They live together in this apartment complex. Jiang is a taxi driver with the license plate 鲁U•T4923, while Shao is a caregiver in a hospital. Jiang went to emergency in a city-center hospital 2 days ago for a slight "brain stem" (脑梗) symptom, and was tested positive as part of routine testing; it's likely his wife was tested immediately afterwards. These were both confirmed positive yesterday.
I feel this indicates the level of testing and contact tracing currently going on in China.