Yes, Richard follows the steps in his story.
1. First, set the scene. Use the Past Continuous. Richard sets the scene by saying "Last week I was waiting for my bus at the bus stop. A lot of people were waiting too, but the buses were late." This uses the past continuous tense ("was waiting").
2. Then, describe the events. Use the Past Simple or the Past Continuous and the Past Simple with when. Richard describes the events using a mix of Past Simple and Past Continuous: "In the end, a bus came and I got on. I sat down and took out my smartphone. I was watching a cat video when the bus stopped. I looked out of the window, but I was in the wrong part of town. I was on the wrong bus!"
3. Finally, describe the result and your feelings. Use the Past Simple. Richard describes the result and his feelings: "I didn't have any money to take another bus, so I walked home. I felt silly and tired but my brother thought it was funny!" This uses the Past Simple tense ("walked," "felt").