Algorithmic management, as a digital management tool in the gig economy, has become a hotspot of concern at the intersection of theory and practice. However, there is a lack of research on the mechanisms and boundary conditions through which algorithmic management affects gig workers’ job crafting. Based on the social information processing theory, this study constructed a dual-mediation model of how algorithmic management influences gig workers’ job crafting through gameful experience and perceived job autonomy. Data from 687 valid samples were collected through a two-stage survey and statistically analyzed using structural equation modeling (SEM). The results demonstrate that algorithmic management increases gig workers’ promotion-focused job crafting behaviors (increasing job resources and challenging job demands) by stimulating their gameful experiences and increases gig workers’ prevention-focused job crafting behaviors (decreasing hindering job demands) by inhibiting their perceived job autonomy. In addition, the higher-order personality trait core self-evaluation moderates the relationship between algorithmic management and gameful experience and perceived job autonomy, as well as the indirect effects of algorithmic management on job crafting through gameful experiences and perceived job autonomy. This study advances empirical research on algorithmic management in the field of the gig economy and human resource management practices. Crucially, it provides practical insights for optimizing algorithmic systems in platform companies, potentially enhancing their efficiency and economic benefits.