People get shot in Texas by someone with intent to kill every year, and these people who are shooting to kill do not get charged with murder and are not convicted of murder.
Therefore the defacto definition of "murder" in Texas is not based on mere intent to kill.
As sipow has pointed out above, there are "exceptions".
Exceptions mean that the definition isn't merely "intent to kill." Some "intents to kill" are legal, and some are not.
But this is putting a finer point on it than most people want to bother, so we just inaccurately accept that "murder" in Texas means "intent to kill", even though there are so many exceptions to this, you can drive a truck through them.
This has become a pointless argument. The woman killed a man accidentally because of her bad judgement, and she deserves to go to prison, and she is going to prison.
Who cares if we use accuracy in meaning? The consequences appear to be the same.
But, the fact that she intended to kill means she didn't commit manslaughter. Guyger was not charged with manslaughter because she didn't "recklessly" cause the man's death. She herself testified that she shot him with the intention to kill.
That's why she was charged with murder (and not manslaughter). If you intended to kill, you didn't commit manslaughter.
Some "intents to kill" are legal, and some are not.
Sure, sometimes people shoot to kill in self-defense, for example. In this case, her attorneys brought up Castle Doctrine as a defense. But, the reality is that Mr. Jean was sitting in his own apartment, and she went into his apartment and killed him. That wasn't self-defense.
Apparently, Texas has only capital murder (where the perp faces the death penalty) and murder (where the perp faces 5-99 years). She was rightfully charged with murder. She was rightfully found guilty.
Apparently, in Texas, after a murder conviction, the jury then takes other factors into consideration when they decide on sentencing. A few of you here were complaining about the murder conviction before she was even sentenced. Now, as you can see, her sentence is pretty much a slap on the wrist.