Generative AI now enables games to produce dialogue, quests, characters, images, and worlds at runtime. Yet generation alone does not make a game AI-native, nor does it guarantee playability. This paper defines AI-native games by whether runtime generative AI is constitutive of the core loop: if the AI component were removed or trivially replaced, the central form of play would collapse or become fundamentally different. This counterfactual criterion separates AI-native games from AI-augmented games, boundary artifacts, chatbots, tavern-style role-play, procedural content generation, and AI-assisted production. Using this definition, we screen candidate artifacts and analyze 53 publicly available AI-native games and prototypes. We introduce a dual-axis G/N taxonomy: the G-axis captures player-facing game type, while the N-axis captures the dominant AI mechanic that makes generative AI indispensable to play. The corpus is concentrated around language-forward designs, especially narrative adventure, epistemic interaction, and generative narrative, while categories such as semantic adjudication, multi-agent simulation, generative construction, and relationship/companion play remain less represented. We argue that the central design problem is organizing semantic openness into stable gameplay. AI-native design depends on mechanical invariants: goals, rules, state, feedback, pacing, and player agency that make open-ended AI outputs interpretable and consequential. We conclude with a roadmap for controllable generation, AI-as-mechanic design, multimodal and multi-agent systems, inference economics, evaluation, safety, and regulation.

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