Narrative visualization has become a crucial tool in data presentation, merging storytelling with data visualization to convey complex information in an engaging and accessible manner. In this study, we review the design space for narrative visualizations, focusing on animation style, through a comprehensive analysis of 80 papers from key visualization venues. We categorize these papers into six broad themes: Animation Style, Interactivity, Technology Usage, Methodology Development, Evaluation Type, and Application Domain. Our findings reveal a significant evolution in the field, marked by a growing preference for animated and non-interactive techniques. This trend reflects a shift towards minimizing user interaction while enhancing the clarity and impact of data presentation. We also identified key trends and technologies shaping the field, highlighting the role of technologies, such as machine learning in driving these changes. We offer insights into the dynamic interrelations within the narrative visualization domains, and suggest future research directions, including exploring non-interactive techniques, examining the interplay between different visualization elements, and developing domain-specific visualizations.