Multimodal Interfaces (MMIs) combining speech and spatial input have the potential to elicit minimal cognitive load. Low cognitive load increases effectiveness as well as user satisfaction and is regarded as an important aspect of intuitive use. While this potential has been extensively theorized in the research community, experiments that provide supporting observations based on functional interfaces are still scarce. In particular, there is a lack of studies comparing the commonly used Unimodal Interfaces (UMIs) with theoretically superior synergistic MMI alternatives. Yet, these studies are an essential prerequisite for generalizing results, developing practice-oriented guidelines, and ultimately exploiting the potential of MMIs in a broader range of applications. This work contributes a novel observation towards the resolution of this shortcoming in the context of the following combination of applied interaction techniques, tasks, application domain, and technology: We present a comprehensive evaluation of a synergistic speech & touch MMI and a touch-only menu-based UMI (interaction techniques) for selection and system control tasks in a digital tabletop game (application domain) on an interactive surface (technology). Cognitive load, user experience, and intuitive use are evaluated, with the former being assessed by means of the dual-task paradigm. Our experiment shows that the implemented MMI causes significantly less cognitive load and is perceived significantly more usable and intuitive than the UMI. Based on our results, we derive recommendations for the interface design of digital tabletop games on interactive surfaces. Further, we argue that our results and design recommendations are suitable to be generalized to other application domains on interactive surfaces for selection and system control tasks.