No-reference video quality assessment (NR-VQA) for gaming videos is challenging due to limited human-rated datasets and unique content characteristics including fast motion, stylized graphics, and compression artifacts. We present MTL-VQA, a multi-task learning framework that uses full-reference metrics as supervisory signals to learn perceptually meaningful features without human labels for pretraining. By jointly optimizing multiple full-reference (FR) objectives with adaptive task weighting, our approach learns shared representations that transfer effectively to NR-VQA. Experiments on gaming video datasets show MTL-VQA achieves performance competitive with state-of-the-art NR-VQA methods across both MOS-supervised and label-efficient/self-supervised settings.