Well, a couple of points: its not obvious that Chinese doesn't have a context-free grammar: see the talk by David Branner: "The Grammar of Classical Chinese

Well, a couple of points: its not obvious that Chinese doesn't have a context-free grammar: see the talk by David Branner: "The Grammar of Classical Chinese is Very Close to Being a Context-Free Grammar". And a properly programmed turing machine can parse languages which are way more complex than context-free languages are.