A key element for the success of any game is its ability to produce a different experience at each round, thus keeping the player engagement high. This is particularly important for those games that also have a serious objective, such as gamified rehabilitation systems, aiming at encouraging patients in performing home rehabilitation exercises. In all cases, a game element which is typically static is the workspace, i.e. the "floor" upon which the game takes place. This is especially true for robot-assisted rehabilitation games, where the workspace must satisfy the requirements given by the robot’s locomotion and localization systems, as well as the patient’s exercise motion requirements. In this article, we present a simple yet effective solution for designing dynamic and customizable tangible workspaces, which relies on hexagonal tiles and our previously proposed Cellulo localization system. These "hextiles" can be easily tangibly rearranged at each game round to yield a desired workspace shape and configuration, allowing tabletop mobile robots to move continuously within each new workspace. We ground our solution in the context of robot-assisted rehabilitation, where high adaptability is crucial for the efficacy of the solution, and propose a dynamic extension of our "tangible Pacman" rehabilitation game. Experiments show that the proposed solution allows for adaptation in range of motions, exercise types, physical and cognitive difficulty, besides reducing repetitiveness.