Story-driven games are growing in popularity across a wide range of genres. However, the narrative potential of video games is still being debated, particularly in light of the so-called tension between gameplay and storytelling. This study proposes that rules and game mechanics perform narrative semiotic functions, offering a ludic grammar of interactive storytelling. Case studies of four representative games show through exploratory player action shaped by rules, the medium of video games can generate meanings that traditional media cannot, thereby better achieving their narrative goals.