Where does the article imply that he didn't know anyone was home?
It says she didn't initially answer the door, which suggests that the answer wasn't immediate, not that it didn't happen at all. (Other articles mention her yelling to her children nearest the door not to open it to a stranger, as she was in a different part of the house when the stranger began knocking/ringing.) It is also worth stating that the burglar was armed with a crowbar.
Also, it should be noted that the police in America have no legal obligation to protect either person or property, unless they specifically extend it to a person. Otherwise they would be liable for any crime thus committed. It should also be kept in mind that even under the best of circumstances, police response times are usually four or five minutes or more. In rural areas, this can increase to upwards of half an hour.
That all being said, while there may have been things that might have been done to further discourage the intruder, that he forced himself into an occupied private residence is justification enough to use a gun. There is a great way not to get shot by homeowners in this country: don't break into their homes. Didn't know someone was home? Well, that problem could have been easily solved by not breaking in.
When an intruder has entered into a private domain, they give those within every reason to fear for their own safety, and the safety of their family. It should not be the duty of a homeowner to, at that point, then determine whether they mean to only break this law or that one, whether they mean to only smash things but also people. A person who has forced themselves into a home is a reasonable risk to the occupants thereof, and a parent not only has the right, they have a moral duty, to protect the family therein in the most effective means available at that time.
By the way: the minimum safe distance for a trained person armed with a gun to be from an aggressor without one is considered to be about 21'. At distances shorter than that, if the person with the gun does not act first then the aggressor is likely able to close the distance before effective stopping
fire can be delivered. Police pratice it with what's called the Tueller Drill.