Good question.
A CCW and stand your ground give you the right to use a sidearm IF you have no other alternative to save your life.
That's not what the Texas law says. SB378 passed in 2007 says that a person is justified in using deadly force against another if he or she believes such force was necessary to protect themselves against the other persons use or attempted use of unlawful force. The law goes on to state that the force is presumed to be reasonable if the person had reason to believe that the other person intended to illegally enter his or her house, vehicle, or workplace. So in this case all the poor guy had to do was storm up to the car and place his hand on the door and she likely had all the justification she needed.