GANs are unsupervised learning algorithms. They use the supervised loss as part of the training.
We know supervised learning is used to predict a label associated with the data. The goal is for the model to generalize new data.
In the GAN case, we don't need either of these components. The data comes in with no labels, and we are not trying to generalize any kind of prediction to new data. The goal is for the GAN to model how the data looks like, and be able to generate new examples of what we learned.
You can use a supervised component for an unsupervised task that is not particularly new. Random Forests have done this for a long time for outlier detection and the One-Class SVM for outlier detection is technically trained in supervised fashion with the original data being the real class and a single point at the origin of the space treated as the outlier class.
Hope this answer helps you! Machine Learning Algorithms, thus will be required for every domain for a better perception of SVM Algorithms.