To interact effectively with humans in the real world, it is important for agents to understand language that describes the dynamics of the environment--that is, how the environment behaves--rather than just task instructions specifying "what to do". Understanding this dynamics-descriptive language is important for human-agent interaction and agent behavior. Recent work address this problem using a model-based approach: language is incorporated into a world model, which is then used to learn a behavior policy. However, these existing methods either do not demonstrate policy generalization to unseen games or rely on limiting assumptions. For instance, assuming that the latency induced by inference-time planning is tolerable for the target task or expert demonstrations are available. Expanding on this line of research, we focus on improving policy generalization from a language-conditioned world model while dropping these assumptions. We propose a model-based reinforcement learning approach, where a language-conditioned world model is trained through interaction with the environment, and a policy is learned from this model--without planning or expert demonstrations. Our method proposes Language-aware Encoder for Dreamer World Model (LED-WM) built on top of DreamerV3. LED-WM features an observation encoder that uses an attention mechanism to explicitly ground language descriptions to entities in the observation. We show that policies trained with LED-WM generalize more effectively to unseen games described by novel dynamics and language compared to other baselines in several settings in two environments: MESSENGER and MESSENGER-WM.To highlight how the policy can leverage the trained world model before real-world deployment, we demonstrate the policy can be improved through fine-tuning on synthetic test trajectories generated by the world model.