Research on live streaming systems that incorporate real-time data, such as game or viewer data, have been a topic of HCI research for some time. Despite the potential of data-driven game streaming interfaces, translating this research into practice faces two key challenges. First, the design space afforded by data-driven game streaming systems is not yet well understood, making it difficult to identify how designs might meet users' existing and potential needs. Second, adoption of these systems relies on engagement with the entire streaming ecosystem, which includes developers, streamers, moderators, and viewers, rather than with just one group. Through a two-phase design study, we investigate the expectations, desires, and experiences of streaming stakeholders, shedding light on how data-driven game streaming systems can meet their needs. Building upon these insights and drawing upon previous research, we propose a design framework aimed at analyzing and generating data-driven game streaming designs, thereby moving toward formalizing the design and development of such systems.