Fake news being spread on social media platforms has a disruptive and damaging impact on our lives. Multimedia content improves the visibility of posts more than text data but is also being used for creating fake news. Previous multimodal works have tried to address the problem of modeling heterogeneous modalities in identifying fake news. However, these works have the following limitations: (1) inefficient encoding of inter-modal relations by utilizing a simple concatenation operator on the modalities at a later stage in a model, which might result in information loss; (2) training very deep neural networks with a disproportionate number of parameters on small multimodal datasets result in higher chances of overfitting. To address these limitations, we propose GAME-ON, a Graph Neural Network based end-to-end trainable framework that allows granular interactions within and across different modalities to learn more robust data representations for multimodal fake news detection. We use two publicly available fake news datasets, Twitter and Weibo, for evaluations. GAME-ON outperforms on Twitter by an average of 11% and achieves state-of-the-art performance on Weibo while using 91% fewer parameters than the best comparable state-of-the-art baseline. For deployment in real-world applications, GAME-ON can be used as a lightweight model (less memory and latency requirements), which makes it more feasible than previous state-of-the-art models.