Analyzing character motivation matters because it goes deeper into the thoughts and feelings of a character in a story or movie. It is more relevant to know what led up to a character doing something than just knowing a character did something. For example I think of the movie Lizzie McGuire with actress Hillary Duff, which was a Disney channel show. Lizzie McGuire as the main character of the show was always seen talking behind the main scenes of the show to say things that was going on in her head. Things she may not have always said to others . You may want to look this up on YouTube or Google to get a better visual.
Character motivation shows the reaction of the characters in certain conflicts and in situation against them. While reading the story, the reader calculates the possible resolutions. In the short story of "Bet", the banker asks questions from himself, namely he self-judges himself. His thoughts on the issue make the reader learn more about him and certainly understand his motives. When he thinks that "On my part, it was the caprice of a well-fed man", it reveals his motivation for the bet. It was aimed for the purpose of entertainment.