Tangible 3D tabletops are a novel type of interface, which combines tangible tabletop interaction with 3D projection in such a way that the tangible objects can be augmented with visual content corresponding to their physical shapes, positions and orientations on the tabletop. We present a specific tangible 3D tabletop installation, Projected Play, which was developed for and deployed at LEGO World, a four-day event at which visitors immerse themselves in the world of LEGO. The use of Projected Play was documented through observations, interviews and video recordings. We propose an analytical approach to understanding the perception and use of this type of installation building upon existing research into interaction in public spaces. We apply this approach to analyse how people interacted with and experienced the installation. The focal points of the analytical approach include social, cultural and physical aspects of experience, interaction patterns and forms of engagement. Moreover, we critically discuss the potentials and limitations of both the analytical approach and the installation.