According to some articles, China is carrying out genocide against the Uyghur people. Others claim it is cultural genocide as its the Uyghur culture that is being eliminated, rather than Uyghurs as a nation. So which one is correct? Is it "genocide", "cultural genocide", neither, or both?
The Convention on the Prevention and Punishment of the Crime of Genocide (the international law defining the crime of genocide) says that genocide is:
In the present Convention, genocide means any of the following acts committed with intent to destroy, in whole or in part, a national, ethnical, racial or religious group, as such:
(a) Killing members of the group;
(b) Causing serious bodily or mental harm to members of the group;
(c) Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part;
(d) Imposing measures intended to prevent births within the group;
(e) Forcibly transferring children of the group to another group.
China has imposed measure to prevent Uyghur births
China has implemented policies designed to prevent Uyghurs from having children, a definition which satisfies item (d) of the definition of genocide. Adrian Zenz, an academic specializing in Chinese politics, authored this document which argues that China's use of forced sterilizations and IUDs for Uyghurs satisfies the legal criterion for genocide. Breaking these birth control laws is punishable by being sent to internment camps. There are also many news outlets online which describe these sterilizations and IUDs, such as this one.
This policy differs from China's more general "one child" policy. Although it uses a case study focusing on Koreans in China, this academic article explains that ethnic minorities were allowed more children. It seems that in many cases the limit was not enforced at all.
Unexpectedly, when the State increased the limit to 2 children per couple nation-wide in 2015, the birth rate for Uyghurs decreased by 84% (Zenz, ibid). Why did it decrease? Zenz (and others) report that enforcement is different. While any ethnicity is theoretically able to be forced to have an IUD, sterilization, or fined, the this punishment is largely saved for ethnic minorities like the Uyghur. Internment camps also appear to be unique for ethnic minorities, which also indicates unequal enforcement in a pretty dramatic way. Internment camps are also used to house family and acquaintances of Uyghurs who do not follow these laws.
An additional tactic reported by Business Insider: when a man is taken to an internment camp, the Chinese government may assign Chinese men to sleep with his wife and live in his house with his family. Although not related to IUD or sterilization, this is another unique policing tactic that is applied unequally to Uyghurs and the ethnic majority.
Outside of the legal argument, there are extant claims that China is systematically killing Uyghurs. I'm presenting this anecdotal evidence because I believe that often first hand accounts are important and under utilized on this site, but also because Uyghurs are an ethnic group that are not commonly encountered in the United States (and I suspect, other western countries).
While at the University of Kansas, I studied Uyghur language where I came to know several Uyghurs from Xinjiang, as well as an extended network of scholars interested in the politics of Xinjiang.
Several of the indigenous Uyghur acquaintances I made have never been heard from since. My instructor, as well as their family and friends, shared their own personal stories of "missing" loved ones, some of which have been missing for a decade or more. In particular, I knew Abduweli Ayup, who was a linguistics student at the time.
Though I can't vouch for the scale of deaths caused by these policies, but this information and my experience with these people supports definition (C). These disappearances are intended to destroy Uyghur people "in whole or in part".
China is actively terminating the future of an ethnic minority:
The Chinese government is taking draconian measures to slash birth rates among Uighurs and other minorities as part of a sweeping campaign to curb its Muslim population, even as it encourages some of the country’s Han majority to have more children.
While individual women have spoken out before about forced birth control, the practice is far more widespread and systematic than previously known, according to an AP investigation based on government statistics, state documents and interviews with 30 ex-detainees, family members and a former detention camp instructor. The campaign over the past four years in the far west region of Xinjiang is leading to what some experts are calling a form of “demographic genocide.”
The state regularly subjects minority women to pregnancy checks, and forces intrauterine devices, sterilization and even abortion on hundreds of thousands, the interviews and data show. Even while the use of IUDs and sterilization has fallen nationwide, it is rising sharply in Xinjiang.
While the above is not mass murder, this is still genocide: "the deliberate and systematic destruction of a racial, political, or cultural group".
Separate but concurrently, China is also systematically assimilating that culture, what is referenced as "cultural genocide" (as per the DW article in the question).
So the answer to the question is both genocide and cultural genocide. But do note that saying "both" implies a kind of equality for both actions, which is wrong.