We present ENGAGE, the first battery-free, personal mobile gaming device powered by energy harvested from the gamer actions and sunlight. Our design implements a power failure resilient Nintendo Game Boy emulator that can run off-the-shelf classic Game Boy games like Tetris or Super Mario Land. This emulator is capable of intermittent operation by tracking memory usage, avoiding the need for always checkpointing all volatile memory, and decouples the game loop from user interface mechanics allowing for restoration after power failure. We build custom hardware that harvests energy from gamer button presses and sunlight, and leverages a mixed volatility memory architecture for efficient intermittent emulation of game binaries. Beyond a fun toy, our design represents the first battery-free system design for continuous user attention despite frequent power failures caused by intermittent energy harvesting. We tackle key challenges in intermittent computing for interaction including seamless displays and dynamic incentive-based gameplay for energy harvesting. This work provides a reference implementation and framework for a future of battery-free mobile gaming in a more sustainable Internet of Things.