Hybrid physical-digital installations in museums are interactive systems or exhibits that seamlessly combine physical (tangible) artifacts with virtual environments. In the museum, hybrid installations offer direct, hands-on experiences to visitors and thus may enhance their interest and engagement. Moreover, the entanglement of tangible and virtual interfaces may reinforce learning about the respective heritage. This article reports on the design, implementation, and evaluation of an interactive installation that promotes the heritage of Tinian marble crafts that is included in the representative list of intangible heritage by UNESCO and resides in the Museum of Marble Crafts in Tinos, Greece. The installation puts the museum visitor in the role of a crane operator in a virtual reconstruction of a historic quarry and requires them to operate the crane and move marble volumes with safety in cooperation with non-playable characters (NPCs). Our design approach aimed to engage visitors in a playful learning experience, incorporating aspects of the two museum's exhibits (crane, quarry). The empirical evaluation took place at the lab and the museum with promising results on UX and learning. In addition, we identify and discuss several prospects and drawbacks of designing playful tangible interfaces for other practitioners to consider in similar applications.