This paper focuses on using a game approach on archeological heritage sites and possibilities for using a location-based game for spatial knowledge acquisition through game space. We propose a location-based game design and a research strategy to decode the spatial information acquisition in the archaeological site sample through user behaviors and cognitive map representations in both spaces (the physical and game space). Our research, part of an ongoing study, presents user experiments' results conducted on the Kültepe Kanesh Karum, Kayseri archeological site, including two setups (sightseeing and game experience) with four participants for each. The collected data includes user traces in the environmental setting using GPS tracking and user experience feedback of sketch map drawings and expressions. Collected data encoded with the spatial legibility parameters (road, node, and landmarks) and interpreted separately and comparatively for both experimental groups. Our initial results indicate the potential of the game space and its effect on acquiring spatial knowledge.