Many states have a thing called felony murder, where if you commit a felony and anyone dies during the commission of that felony, you get charged with their murder. So if you steal a car and crash into someone, killing them, that's felony murder... If you and your friend rob a house and a police officer shoots your friend, felony murder. If you rob a bank and the bank teller has a heart attack, felony murder. Etc.
In this case, unauthorized driving is a felony in Texas, and this kid killed this innocent women during the commission of that felony, thus felony murder.
The "fleeing" someone is irrelevant. They egged that person's car, which is at the very least vandalism, possibly even destruction of property if the car was damaged. The man had every right to pursue those who vandalized his property. The felony the pursuing driver faces is for failure to stop and render aid; since he was tangentially involved in the accident, he had a duty to stop and render aid.