The advent of artificial intelligence (AI) and machine learning (ML) bring human-AI interaction to the forefront of HCI research. This paper argues that games are an ideal domain for studying and experimenting with how humans interact with AI. Through a systematic survey of neural network games (n = 38), we identified the dominant interaction metaphors and AI interaction patterns in these games. In addition, we applied existing human-AI interaction guidelines to further shed light on player-AI interaction in the context of AI-infused systems. Our core finding is that AI as play can expand current notions of human-AI interaction, which are predominantly productivity-based. In particular, our work suggests that game and UX designers should consider flow to structure the learning curve of human-AI interaction, incorporate discovery-based learning to play around with the AI and observe the consequences, and offer users an invitation to play to explore new forms of human-AI interaction.