Creativity is recognized as an essential skill in 21st-century education. Storytelling can facilitate student motivation, engagement, and cognitive development. However, conventional storytelling approaches often lack interactivity and fail to capture learners' attention. According to Self-determination Theory (SDT), satisfying basic psychological needs (i.e., autonomy, competence, and relatedness) is essential for fostering motivation and well-being. This study examines how a multi-sensory digital storytelling system incorporating an interactive robot affects student engagement and psychological well-being compared to paper-based and PowerPoint (PPT) modalities. The research addresses the gap in exploring how different storytelling delivery modes influence students' intrinsic motivation and performance in well-being. Twenty-four students (12 female, 12 male) aged 7-8 years participated in a comparative study in three conditions: paper-based storytelling (n=8), PPT-based storytelling (n=8), and robot-assisted storytelling (n=8). A human-like robot is equipped with multisensory support, including animations, instant feedback via a large language model (LLM), and interactive movements. The five-day intervention delivers one story per day. Students complete pre- and post-questionnaires and conduct semi-structured interviews to provide insights into emotional experiences and learning preferences. The robot-assisted group demonstrates statistically significant improvements in behavioural (pre: μ=70.83, σ=18.15; post: μ=90.00, σ=9.43; +27.06%, p<.05) and cognitive engagement (pre: μ=66.67, σ=18.86; post: μ=86.67, σ=10.08; +30.00%, p<.05). Qualitative findings reveal that students express excitement, reduce frustration, and feel confident interacting with the robot. Interactive robot-assisted storytelling significantly enhances behavioural and cognitive engagement and promotes psychological well-being. The integration of multisensory and interactive technologies aligns with SDT principles to foster intrinsic motivation and happiness. Future longitudinal research with larger samples will strengthen these findings and explore sustained effects on well-being.