China's supervision of health food is still implementing the relevant provisions of the Measures for the Administration of Health Food, but the Measures for the Administration of Health Food is formulated according to the now abolished Food Hygiene Law of People's Republic of China (PRC), and the Food Safety Law of People's Republic of China (PRC) is implemented. The Regulation on the Supervision and Administration of Health Food formulated according to the Safety Law is seeking opinions and will be promulgated in the near future, and the Measures for the Administration of Health Food will be abolished in the next session. The relevant provisions are as follows:

Health food refers to foods that claim to have specific health functions and are approved according to law. Health food should be suitable for specific people to eat, with the function of regulating the body, not for the purpose of treating diseases, and not causing acute, subacute or chronic harm to the human body.

Health food shall be examined and approved by the State Food and Drug Administration in accordance with the law and obtain the product registration certificate. The health food that has obtained the product registration certificate shall use the health food mark specified by the state food supervision and administration department.

Except the health food that has obtained the product registration certificate, other foods may not claim the health function or publicize and sell in the name of health food.

If the food that has not obtained the registration certificate of health food products claims to be functional and counterfeit health food, the food and drug supervision and administration department shall investigate and deal with it according to law.

Obviously, the yogurt product you mentioned is not registered as a health food and does not belong to the category of health food. Of course, they can't claim to have health care functions.