Go for the throat is an idiomatic expression (not a phrasal verb).
The following definition can be seen in more detail here:
To engage in an aggressive attack against someone without holding back
or showing any mercy; to attack the most vulnerable part of someone.
The phrase is usually (though not always) understood as referring to a non-physical attack. Similar to the phrase "go for the jugular."
This is politics, and the candidates aren't going to play nice during
the debate—they're going to go for the throat any chance they get.
If you tangle with him, don't expect a fair fight—he'll go for the
To answer your interesting question:
"Go for the throat" is used figuratively here. Who goes for the throat? Laura Marks, the screenwriter. Whose throat does she do for? She goes for the throat of each viewer. What does it mean? The screenwriter writes stories that aggressively reach the most vulnerable part of each viewer's psyche.
We would therefore expect this story by Laura Marks to touch deep personal issues in a powerful way. Many viewers are very likely to be moved by this particular story because it really goes for the throat.