The law however doesn't typically let you chase people and shoot them after the robbery is over.
While some states may still have an obligation to retreat, you most certainly have the legal ability to chase a robber in an attempt to stop a crime that is still in progress and/or to recover stolen items. Additionally, lethal force may be used when such force is threatened by the bad guy. In this case, the bad guy drew a gun. At that point, the CCW holder definitely had the legal right to defend himself with lethal force. This issue at that point had nothing to do with the woman being in jeopardy.
Also, it may well be argued that since the CCW holder had witnessed the attack where the woman was struck in the head with the gun that the suspect in flight posed a threat to public safety.