Gaze interaction in games moved from being a tool for accessibility to be at the core of mass-market game franchises, offering enhanced controller performance and greater immersion. We propose to explore three different popular gaze-based interaction mechanics to create novel opportunities in the game design space. We developed Twileyed, a collection of three games that challenge the "common" use of gaze as a pointer to navigate; select; and aim; to pose a challenging new way to play with the eyes. We used the games as data to reflect on the gaze design space. We asked users to play the games to validate them, and we observed their experience and strategies. Based on the observations, we discussed through 5 themes, the dimensions of gaze interactions and the potential outcomes to create engaging and playful gaze-enabled games. We contribute a position in gaze gameplay design, but also a conversation starter to engage the EyePlay research community.