Hi. You have not submitted the essay this question refers to, which makes it impossible for it to be answered. However, I will try and help as best I can.
It is only possible to know how the reference to King Midas is important for the essay if the reading of the essay is done. However, King Midas is known to be a very ambitious and wealth-obsessed King, even to the point of selling his own soul to become richer, which causes him to lose his most precious possession, his daughter. In this case, we can consider that the essay must present this king to draw a parallel between the subject of the essay and this tragic story of Midas, stimulated by the thirst for riches. We can therefore consider that the reference to Midas serves to intensify some of Chesterton's positions within the essay.
This is an example of an allusion, because an allusion is a figure of speech that allows a text to make references to other texts, people, characters, places and external situations.
The sentences write after his story shows the family's initial reaction which is mostly doubtful from the son and the wife
that was a good story!
