Depends on the jury.
Texas Penal Code Sec. 19.05. CRIMINALLY NEGLIGENT HOMICIDE. (a) A person commits an offense if he causes the death of an individual by criminal negligence.
~ (b) An offense under this section is a state jail felony.
After reviewing the Statute you are probably right. Under the Texas Penal Code the negligence must be "criminal negligence", which I suspect must include the breaking of a law, such as speeding, drunk driving, fighting.
So in this case there is virtually no chance he will be charged.
As I often say, I've been wrong before. Here's an example.
This discussion is an intellectual exercise, however, because the guy is not likely to die. Cheney got lucky here. He needs remedial hunters safety instruction.