You could say it's ironic because most people would presume that an unmarried man would not have a clue about children and how to entertain them. This is exactly what the aunt presumes. She even presumes that the man is frowning because of the children's behavior, labeling him as “unsympathetic” when he is most likely frowning at her and her own reaction to the youngster's question about sheep.
However, it isn't that unusual that someone like him, an outsider in terms of the world of the family, would understand the children better. How many people, for example, can remember an unmarried aunt and uncle entertaining them silly? Like the man in the story, they always seemed to have a better understanding and more unique take on the modern world.
In addition, there is no consequence to their actions. The man can tell a story about a wolf eating a girl because she is just too good and then walk off the train, knowing he won't have to deal with the children later. The aunt, on the other hand, like so many parents, probably knows the consequences her words and actions can have. She may seem unimaginative in the context of the story, but she could just as easily be trying to do her best by the children.
In that context, the irony comes from the fact that the children are taken in by someone aiming to do them more harm than good.
At the end of the story the man states:
"Unhappy woman!" he observed to himself as he walked down the platform of Templecombe station; "for the next six months or so those children will assail her in public with demands for an improper story!"