The words premeditation or premeditated do not appear in that statute. In fact they don't appear in the Texas Penal Code at all. That statute is talking about intent, which is an element of any crime in the Texas Penal Code. In states that have premeditation or malice aforethought as a part of their homicide laws, it is generally defined as forming the intent to kill in advance over a period of time that would allow reflection on the situation, but that varies from state to state.
Here is a quick, general summary of Texas Homicide laws:
Murder: A first degree felony punishable by 5 years to Life. Defined as intentionally or knowingly causing the death of a person. Alternate definition is intending to cause serious bodily injury to someone and causing their death by committing an act clearly dangerous to human life. This is basically so you can't shoot and kill someone and claim you were just trying to wing them and not kill them. Other alternate definition of murder is known as "felony murder" which is when someone is intending to commit some other felony and in doing so does an act clearly dangerous to human life that causes the death of a person.
Sudden Passion: This is a punishment issue. After someone is convicted of murder, in the punishment phase, if the Defendant proves by a preponderance of evidence that he was under the immediate influence of sudden passion resulting from an adequate cause, it lowers the range of punishment to 2 to 20 years. The common example given to illustrate this is a guy finding his wife in bed with another man and shooting the dude.
Capital Murder: a capital felony punished by Death or Life without parole, or Life with parole eligibility after 40 years for 17 year olds. This is basically intentional Murder plus an aggravating factor such as killing a cop, or killing more than one person, or killing a kid, or killing someone while committing a robbery, etc. There are several other circumstances in Penal Code Section 19.03. But that isn't really relevant to this case as far as I know.
Manslaughter: second degree felony, 2 to 20 years. Recklessly causing a death. Recklessness is when you are aware you are doing something that creates a substantial and unjustified risk and you do it anyway.
Criminally Negligent Homicide: Causing a death by criminal negligence, which is when you should have known what you were doing created a substantial and unjustified risk.
Self-Defense: This is a defense that the defendant has to raise at trial and the state has to disprove beyond a reasonable doubt to get a conviction. To simplify it as much as possible, it is when you intentionally or knowingly cause someone's death but you were justified in doing so because you REASONABLY felt it was immediately necessary to defend yourself from the other person's use or attempted use of deadly force against you. To boil it down further, the jury takes in all the facts and they decide whether what the person did was reasonable given the circumstances. You can only use deadly force (ie a gun or knife or deadly weapon) if you are faced with someone using deadly force against you. However, that doesn't mean you are automatically guilty if the other person wasn't armed. Usually the defendant will say the other person was capable of killing or seriously injuring them without a weapon, ie with fists. Or they will say they were under the impression the other person was armed for some reason (apparent danger.) It is ultimately up to the jury to decide whether it is REASONABLE. Personally, I wouldn't think it is reasonable to stab someone in the heart if they pushed you or you are in a fistfight with them, but it is ultimately up to the jury.