In the example you provided, the most influential story element appears to be characterization, particularly the relationship between Mike and his brother. Mike's patience and determination to wait for the rain to stop contrast with his brother's impatience. This dynamic can drive the plot forward and reveal themes such as sibling relationships, resilience, and contrasting personalities.
Additionally, setting (the tree and the rain) plays a role in creating the mood and may influence the actions and decisions of the characters. However, the interaction and characteristics of the characters seem to be the primary focus that influences the story's development.