Reinforcement Learning (RL) faces significant challenges in adaptive healthcare interventions, such as dementia care, where data is scarce, decisions require interpretability, and underlying patient-state dynamic are complex and causal in nature. In this work, we present a novel framework called Causal structure-aware Reinforcement Learning (CRL) that explicitly integrates causal discovery and reasoning into policy optimization. This method enables an agent to learn and exploit a directed acyclic graph (DAG) that describes the causal dependencies between human behavioral states and robot actions, facilitating more efficient, interpretable, and robust decision-making. We validate our approach in a simulated robot-assisted cognitive care scenario, where the agent interacts with a virtual patient exhibiting dynamic emotional, cognitive, and engagement states. The experimental results show that CRL agents outperform conventional model-free RL baselines by achieving higher cumulative rewards, maintaining desirable patient states more consistently, and exhibiting interpretable, clinically-aligned behavior. We further demonstrate that CRL's performance advantage remains robust across different weighting strategies and hyperparameter settings. In addition, we demonstrate a lightweight LLM-based deployment: a fixed policy is embedded into a system prompt that maps inferred states to actions, producing consistent, supportive dialogue without LLM finetuning. Our work illustrates the promise of causal reinforcement learning for human-robot interaction applications, where interpretability, adaptiveness, and data efficiency are paramount.