When describing a restaurant, you use an adjective. Thus, the adjective Chinese describes the nature of the restaurant. Similarly Indian Restaurant, Thai Restaurant etc.
China in this usage is a noun and so is not appropriate in this type of phrase.
(Although another meaning of China is an adjective describing something made of ceramic)
There is an alternative description for restaurants that uses a noun phrase rather than an adjective. This is when a specific food is served, rather than a style of food. Examples are Burger Restaurant or Pizza Restaurant.