One of the best ways authors generally bring out the theme of conflict in their writing is to portray a struggle between opposing values.
For example, in this short story, Conradin and his guardian both hold completely different views about life and happiness; this just means that they don't share the same personal values. Therein lies the conflict. Despite his seeming physical affliction, Conradin wants to live a normal life. Additionally, he is lonely and bereft of affection. His guardian doesn't understand him; her myopic beliefs about respectability fail to take into account Conradin's emerging individuality and personal inclinations.
Every Thursday, in the dim and musty silence of the tool-shed, he worshiped with mystic and elaborate ceremonial before the wooden hutch where dwelt Sredni Vashtar, the great ferret. Red flowers in their season and scarlet berries in the winter-time were offered at his shrine, for he was a god who laid some special stress on the fierce impatient side of things, as opposed to the Woman's religion, which, as far as Conradin could observe, went to great lengths in the contrary direction.
The paragraph above clearly illustrates the discrepancy between the two. Their values are so different as to cause them to engage in a consistent battle of wits. Conradin is too young to understand Mrs. De Ropp's motivations, and because she hasn't seen fit to engage her charge in any sort of meaningful communication, her actions descend to the level of petty cruelty in our eyes.
An example is when she tells Conradin that 'the Houdan hen had been sold and taken away overnight.' Mrs. De Ropp is ready to 'rebuke with a flow of excellent precepts and reasoning' should her charge make a scene. This is Mrs. De Ropp's usual modus operandi; she exhibits little respect for Conradin's happiness and little consideration for his preferences. She will, however, criticize, scold, and condemn if Conradin puts up any sort of a fuss.
This is how Saki cleverly brings out the theme of conflict in his short story: he juxtaposes Mrs. De Ropp's disrespect for Conradin's values with Conradin's disgust towards his guardian's seemingly misguided code of ethics.