In this paper, we introduce the notion of beaver-play to understand play that challenges spatial conventions, transgresses boundaries, and redraws territories. Tracing how beavers are imagined in various contexts such as nature conservation, experimental rewilding practices, and performance art, we highlight the role of the beaver in stories of ecosystem management, collapse, and restoration. We investigate beaver imaginaries through the perspective of play and games, taking the popular citybuilding video game Timberborn as our case study. We employ sketching as a method to annotate and analyse play practices in the digital spaces of Timberborn, drawing out three modes of beaver-play: concerns, crossings, and flows. Highlighting the role of play in territorial and organisational fluidity, we draw attention to the way that beaver-play scaffolds moving in and out of spatial arrangements, territories and environmental systems. Discussing how the practices of playing and drawing intertwined into a process of more-than-human cartography, we extend our investigation to consider the broader implications of using video games as cartographic, performative spaces for more-thanhuman meaning-making.