No.
Noem got extreme blowback from MAGA/Republicans after this came out. It instantly ended any chance she had of being the VP.
Why she thought people would be impressed by that story is beyond me.
She got from that story exactly what she wanted: a cabinet position.
1. Let's illustrate the idea of subtext with an example: Have you ever read the bible? You know how some of the stories seem, well, trivial if you take them at face value? Let's consider the parable of the Judgement of Solomon -- the famous story about two moms who both claim to be the baby's mother, and Solomon proposed cutting the baby in half, at which point the true mother revealed herself. Why would that completely insignificant story be included in the history of the Jewish people? Moses parted the red sea. The Jewish people had powerful military triumphs but also heartbreaking defeats. Sometimes God created miracles. And also, this one time, the king didn't kill a baby.
So that's weird and bizarre, isn't it? It's especially weird that, in the story, the mothers acted idiotically. The idea that the fake mother would agree to accept "half" of the severed child is absolutely nuts (also, who would have severed the child in two? What technology would have made that possible? The king was really going to order a soldier to split a baby in two with an axe?). It obviously didn't happen that way. Nor would the real mother simply renounce her claim, unless she thought Solomon was a bloodthirsty tyrant who meant what he said about splitting the baby -- and that would be a strange thought, given that the story and many others are specifically demonstrating that he was not such a tyrant.
Obviously, the story is metaphorical. We're not supposed to think of the baby literally. Rather, the baby represents something else. A lot of people, as far as I know, think that the baby is a metaphor for the Jewish people. The story thus describes the nature of leadership, and it also sets forth the values that define the Jewish people: empathy and sacrifice. The baby-splitter mom symbolizes a nakedly transaction view of the world, in which the goal is to get your share regardless of what is required. Solomon realizes that's not the society God wants.
[Note: there plenty of other subtextual stories in the Bible that work somewhat similarly -- Abraham and Isaac for instance.]
2. So, what's the subtext of Noem's story? Like the Solomon story, it's meant to describe a form of leadership -- but one that is very different in nature, given that Solomon preserved the baby and Noem killed the dog. Both stories are trying to communicate a leadership principle. Solomon shows that empathy is a defining aspect of the Jewish religion. Noem is trying to show that she's cold-blooded enough to kill when it's needed.
Why does she call the dog "extremely dangerous"? It obviously wasn't. It looked like a puppy, but deep down it was a killer that needed to be put down. Hmm, who does that resemble? Oh, yes: migrants. They seem like innocent people who come to the US to escape oppression and who just want to earn money for their families -- but Trump and the GOP claim they are anything but. They are a sinister shadowy group of people who are extremely dangerous, who are invading our country, whose gangs take over towns and terrorize the residents. Now, it would be especially bad form for Noem to brag about killing a human, so she demonstrates her lack of empathy by killing a dog.
Does this interpretation of the story -- i.e. as a parable about jettisoning toxic empathy -- fit Noem's later actions? Oh yes it does. Look at her cosplay at the El Salvador prison. She killed the dog because it had to be done to protect. They shipped the people to El Salvador without due process, because it had to be done to correct. She was advertising her heartlessness, which is exactly what Trump wants out of DHS.
3. So does it make sense now why she included the story? It wasn't an accident and it wasn't a bad judgment. She knew what she was communicating, and it was in fact communicated to the person who cared.