As large language models (LLMs) become increasingly persuasive, there is concern that people's opinions and decisions may be influenced across various contexts at scale. Prior mitigation (e.g., AI detectors and disclaimers) largely treats people as passive recipients of AI-generated information. To provide a more proactive intervention against persuasive AI, we introduce $\textbf{LLMimic}$, a role-play-based, interactive, gamified AI literacy tutorial, where participants assume the role of an LLM and progress through three key stages of the training pipeline (pretraining, SFT, and RLHF). We conducted a $2 \times 3$ between-subjects study ($N = 274$) where participants either (1) watched an AI history video (control) or (2) interacted with LLMimic (treatment), and then engaged in one of three realistic AI persuasion scenarios: (a) charity donation persuasion, (b) malicious money solicitation, or (c) hotel recommendation. Our results show that LLMimic significantly improved participants' AI literacy ($p < .001$), reduced persuasion success across scenarios ($p < .05$), and enhanced truthfulness and social responsibility levels ($p<0.01$) in the hotel scenario. These findings suggest that LLMimic offers a scalable, human-centered approach to improving AI literacy and supporting more informed interactions with persuasive AI.