This young lady didn't have a chance to find out what the jerk wanted. He tried to climb in her vehicle and she started fighting immediately. At least in a public place she had a chance. With this type of attack, it's very likely that he was not there to take a purse (even though he left with it), but to try and abduct his chosen victim.
Also, (if practical) get a gun. Practice with the gun. Carry the gun (permitted if applicable). Most importantly, be mentally prepared to use the gun. If that's not practical, research legal methods of defense in your area (knife, kubotan, pepper spray). An immediate violent response of any kind can turn the tables on an attacker quicker than you think is possible.
I just watched the interview on TV (not shown in the video with this story) with this young woman and as she got emotional, she said she screamed and "Nobody saw, nobody came. I must have been in my car struggling for what seemed like eternity because I was there for a while trying to fight him off. Nobody saw and it was really busy for a Monday at HEB. Nobody heard anything. It was like they wanted to ignore it." She finally got her fingernails in his eyes and drove him away.
This. This is why you must be prepared to defend yourself. The good Samaritan mentioned in the article became involved after the perp had already stabbed her in the neck a few times and was trying to get away. Unfortunately, not everyone will come swooping in to rescue you. There are many studies and videos showing people standing around and watching terrible things happen. Only you can protect you. She is now fearful about possible retribution from the scum that attacked her. Empower yourself. Protect yourself.
The interview is not posted on the internet, yet. I will post it when it is available. It is emotional and quite powerful. She saw him coming before he entered the vehicle. She was able to fight him while in the vehicle. Situational awareness and proper deployment of a firearm from retention would have ended this and she would not be living in fear right now.
Be safe out there.