As a hedonic technology, short-form videos (SFVs) have attracted numerous users. However, one related problem that merits research is SFV addiction, especially among adolescents due to their immature self-control abilities. Although recent research has discussed the formation process of SFV addiction from psychological needs and the SFV features perspective, scarce attention has been paid to investigating the relationship between stress and SFV addiction, as well as the relationship between SFV addiction and its consequences. Therefore, the purpose of this study is to examine whether school burnout (school stress), social phobia (social stress), and parental phubbing (family stress) trigger SFV addiction based on stress-coping theory and, furthermore, whether SFV addiction leads to low levels of happiness (psychological consequence), parent–child relationship quality (relational consequence), and perseverance (behavioral consequence) among adolescents. The proposed model was tested based on data collected from 242 adolescents from across China under the age of 18 with the experience watching SFVs. A covariance-based structural equation modeling (CB-SEM) method was used for data analysis. The results showed that school burnout and social phobia significantly triggered SFV addiction, which later negatively and significantly influenced adolescents’ happiness, parent–child relationship quality, and perseverance. The study also found that SFV addiction served as a mediator between the drivers and consequences of SFV addiction. This study provides several theoretical implications. First, this study is one of the first to explain adolescents’ SFV addiction from stress-coping perspective, thereby enriching research in the field of SFV addiction. Second, prior research has rarely discussed the impacts of stresses from various environments on addiction behavior in a single study. Therefore, this study contributes to the knowledge of stress-related research in an SFV addiction context. Finally, our study enhances our understanding of the impact of SFV addiction on its consequences, in both an SFV research context and a social media research context.