Some caveats to that advice:

Thus, if someone sticks a gun in your face and demands your wallet, you should hand it over without hesitation—and run.

That depends; statistics say those who resist violent crime have better outcomes. It's something you should play by ear rather than blindly follow the above advice, the statistics are undoubtedly biased by people resisting when it makes sense.

Even if you are at home, in possession of a firearm, and well trained to use it, when confronted by an intruder your best defense is to get out of the house as quickly as possible. In such a circumstance, a gun is a means of ensuring that no one can block your exit.

This above is very iffy advice. Not only do you have much stronger legal protections inside your house, you're likely to have much greater control over the situation, and control is perhaps his main message. You know your house, can benefit from concealment and maybe even cover (that which a bullet cannot penetrate), you don't know the situation outside the house. You might escape only to be surprised by an armed accomplice. Or suppose you do this just as the police arrive; more than a few armed homeowners have gotten shot by police mistaking them for criminals.

You also need to balance this advice about decreasing the risk to your physical skin with the psychological toll fleeing takes.

Nothing good ever comes to people who allow themselves to be moved to a remote location at the mercy of a violent predator.

In my Missouri concealed carry class they ran us through a simulator with police "shoot/don't shoot" scenarios. For mine, I would have been a lot more aggressive and would have tried to shoot at various times if I'd know the terrible statistics of the above which the instructor mentioned after it.

As for his advice to flee and leave your spouse or children to the tender mercies of someone who, as he notes, has demonstrated he wants more than your property, if you have any other option I don't want to know you. That includes your being in such a situation because you decided not to procure one or more firearms prior to the incident.

After I left home, I only procured firearms after I had a significant other to protect, or vice versa. At that point it was an obligation, no matter what obstacles Massachusetts put in place (which aren't really that bad for long guns, although that may be changing depending on the city you live in).

On the other hand, I picked up a very hard rule about hostages from Jerry Pournelle in The Mote in God's Eye: at that point, you mentally treat the situation as if the criminal has killed the hostages, even if you then try to rescue them. In this situation, as the author says, you don't increase the toll by submitting yourself as well. The odds are very high that will make the situation worse.

Final note, underlying a lot of what he says: if someone unknown knocks on the door, I don't answer without having a gun in my hand. If I'm expecting someone, I confirm it's them before opening the door. Or per a rule of Marine general James Mattis WRT to being in Iraq or Afghanistan during our recent unpleasantness, which addresses even more points the author made: "Be polite, be professional, but have a plan to kill everybody you meet."