First, their focus is on politics and not religion.

Second, you don't go to Spain and deliver the gospel speaking German. When Paul was in Athens he was able to relate by talking about the unknown god.

Third, when Matt was lamenting the changes in the way we approach church, by moderating the message, I could relate. Some yeast and salt is effective.

Hold on, I see where this author is coming from on some of the later points but I don't understand the issue on the main point... Is it not correct that using the Bible to argue against abortion does not work on someone who does not believe in the Bible's authority? That person very likely believes in logic and reasoning, because they are a part of a Judeo-Christian society, but they don't believe in God. So logic and reasoning are going to be more effective on them than arguing about God.

The gun scenario is strange to use here and it kinda helps make Matt's point in a strange way. Convincing them that the gun is real and that attacking his family is wrong is definitely a way to try and get them to stop attacking, but it takes all of this extra work and time. If convincing the assailant that the gun is real will not work in time to save his family, then he will shoot away. They likely can't ignore their physical body and pain signals, so shooting them should work... And this is ignoring the fact that the gun is in material reality and the Bible is referring to metaphysics, which make the two incomparable.

Now I'm not a trained philosopher, so I may have some things that "technically" don't fit with the "Argument from Authority", but I still think it's common sense to say that an athiest won't listen to arguments from God.