""A person commits the offense of murder if the person 1) intentionally or knowingly causes the death of an individual or 2) intends to cause serious bodily injury and commits and act clearly dangerous to human life that causes the death of an individual." Her testimony is that she intentionally and knowingly caused the death of an individual.
Manslaughter or reckless homicide if there isn't.
First, there's no such thing as reckless homicide in Texas law. Second, the law on manslaughter is "a person commits the offense of manslaughter if she recklessly causes the death of an individual. A person acts recklessly or is reckless with respect to the result of her conduct when she is aware of but consciously disregards a substantial and unjustifiable risk that the result will occur. The risk must be of such a nature and degree that its disregard constitutes a gross deviation from the standard of care that an ordinary person would exercise under all the circumstances as viewed from the actor’s standpoint." Did she consciously disregard that the result of her shooting the victim would be his death? No, her own testimony was that she aimed and fired intending to kill.
You've left something out. There are plenty of people that kill someone intentionally and knowingly yet are not accused or convicted of murder.
Ergo, the definition is not correct, or is incomplete.