The fundamental characteristic that digital games have is interactivity. Digital games need to be systematically categorized so that similarities and differences can be identified and analyzed. Research in the past, however, has not established common criteria for categorizing digital games. This paper resolves that gap by identifying the fundamental characteristic of games, interactivity, and develops a conceptual framework consisting of primary and corresponding participants, and controlling characters. Through an empirical analysis on some digital games, this study shows that the framework could be comprehensive covering all of interactivity during the game. Future research topics are presented based on this framework.