This is the 1530th most frequent German word.
chinesischen
"Chinesischen" means "Chinese" (adjective, referring to something from China).
The word 'chinesisches' here is used as an adjective, modifying the noun 'Buch' to specify its origin or type.
Ich habe ein chinesisches Buch gekauft.
I bought a Chinese book.
The word 'chinesische' functions as an adjective, describing the noun 'Küche' to denote the cultural origin of the cuisine.
Die chinesische Küche ist weltweit bekannt.
Chinese cuisine is known worldwide.
The word 'chinesisch' in this context is used as an adverb, referring to the language being spoken and its fluency.