There are many kinds of arguments. Some arguments are psychological, not related to "winning" but understanding what makes the interlocutor tick.

The article is formulaic. It doesn't make it inherently bad.

The presenting of a persona interaction, followed by a recipe on how to deal with that, is one of those discussion tricks. Whoever answers must put itself in either the toddler's position or the adult position. Both positions are disfavorable (they're flat stereotypes)

The author is actually playing neither, it is acting as an "overseer" of silly toddlers and silly adults that engage in arguments all wrong.

It is a curious thing how far these things went.

Tantrums can happen for all kinds of reasons, and adults can engage in fruitless argument for all kinds of reasons too. It's a human thing. Sometimes, even in perfectly reasonable discussions, no one learns anything. That is also a human thing.

Changing one's point of view is something dramatic. To expect that in an argument is unreasonable, it's too high of a goal.

Just making the other part understand the subject is a lesser, more attainable objective. They don't need to agree. Sometimes I feel glad when I notice that the other part found the core of the discussion, even if they are in opposition to my view. It means that they understood the subject, which is something rare these days.