Assessing the visual quality of video game graphics presents unique challenges due to the absence of reference images and the distinct types of distortions, such as aliasing, texture blur, and geometry level of detail (LOD) issues, which differ from those in natural images or user-generated content. Existing no-reference image and video quality assessment (NR-IQA/VQA) methods fail to generalize to gaming environments as they are primarily designed for distortions like compression artifacts. This study introduces a semantically-aware NR-IQA model tailored to gaming. The model employs a knowledge-distilled Game distortion feature extractor (GDFE) to detect and quantify game-specific distortions, while integrating semantic gating via CLIP embeddings to dynamically weight feature importance based on scene content. Training on gameplay data recorded across graphical quality presets enables the model to produce quality scores that align with human perception. Our results demonstrate that the GDFE, trained through knowledge distillation from binary classifiers, generalizes effectively to intermediate distortion levels unseen during training. Semantic gating further improves contextual relevance and reduces prediction variance. In the absence of in-domain NR-IQA baselines, our model outperforms out-of-domain methods and exhibits robust, monotonic quality trends across unseen games in the same genre. This work establishes a foundation for automated graphical quality assessment in gaming, advancing NR-IQA methods in this domain.