As a member of NATO, Turkey can ask the Americans to deploy Patriots batteries, along with operators, immediately to defend them from attack. China has no such obligation, and any HQ9 missiles would need to be bought and paid for by Turkey, and Turkish personnel would need to be trained to operate them.
Why would Turkey paid for something that would only be operational maybe years down the line, when they can ask their NATO allies for it for free and to be deployed immediately?
Although it will be a tough ask for the Turks to convince anyone that this would be a defensive necessity since their soldiers are getting killed on sovereign Syrian soil, and any NATO SAM batteries wishing to defend Turkish forces inside Syria would be firing into Syria on Syrian government forces. That is an act of aggression and war.