This research investigates the key factors influencing young users’ continuous use of digital twin-enhanced metaverse museums. Attracting young users to use the metaverse museum for a more extended period consistently contributes to increasing the frequency of visits and content usage and promoting its sustainable development and innovation. However, there is a lack of research on the key factors influencing young users’ continuous use of digital twin-enhanced metaverse museums, which makes the theoretical basis for the in-depth design of user motivation for metaverse museums insufficient. This study constructed a model covering four dimensions—hedonic, utilitarian, social, and technological—based on communication’s uses and gratification theory (UGT). It was validated in the Metaverse Digital Twin Museum (MDTM). Using Spatial.io’s IES Goya Museum as the experimental platform, the research team conducted Partial Least Squares Structural Equation Modeling (PLS-SEM) using SmartPLS 4.0 software through experiments and surveys with 307 participants aged 18 to 30. Quantitative analyses revealed that MDTM’s hedonic gratification (hope), utilitarian gratification (information and self-presentation), social gratification (social interaction and social presence), and technological gratification (immersion) significantly influenced young users’ continued intention. The findings reveal that these six key factors can be the focus of MDTM’s future development to enhance user experience. This study fills the gap in applying UGT in the field of metaverse museums, provides metaverse museum managers with references to the key factors that can prolong users’ continued intention to use, and points out the key factors that need further attention in future research and practice.