Participatory practices rely on group discussions to elicit information and shared understandings about systems under consideration, often employing representations such as conceptual models to help make sense of complexity. However the semantics of such models are often unclear, and a lack of participation in their creation can negatively impact their sense-making potentials. Ontologies can aid in multi-stakeholder engagements through semantic alignment, yet these can be difficult to learn and apply, adding more complexity to participation activities. This paper attends to these challenges by incorporating aspects of game and play to mediate expertise discourses through shared, cooperative, and playful experiences. It presents an exploratory case study of game-based group modelling using ontology-based models, reporting on two purpose-built group modelling games and their deployment in a conference workshop. The analysis of workshop outcomes examines in-game modelling, individual models, and corresponding model pairs, using qualitative discourse analysis techniques. Supplementary pre- and post-experience questionnaires and ethnographic observations elaborate the advantage of combining modelling, ontologies and games to foster and visualise shared understandings. This research sets a baseline for the study and development of participatory, ontology-based group modelling, and the examination of conceptual models as texts in multi-modal discourse analysis.