A paradox is a literary term that is used to describe something that is literally a contradiction in terms. A great example is describing somebody as a "wise fool," which obviously, at face value, appears to be meaningless as the two words appear to contradict each other. However, paradoxes always hide a deeper reality that ask us to look again at what is being described and to see the truth that is contained therein.

In the quote you have cited from this excellent short story, the paradox is the way in which for the narrator, the "serious work of life" now appears to be nothing more than "child's play," which of course is a contradiction in terms. However, this paradox helps us to understand the way in which the romantic quest that he has been given by Mangan's sister has dominated his imagination and every moment of his thinking, resulting in his focus on that alone and his forgetting of his studies. This paradox is therefore used to help build up our picture of the character of the narrator and how he is consumed by his romantic quest.