You are right about autoencoders and the architecture with the latent variables in the bottleneck.
However, in the DCGAN setup you have basically a generator (G) and a discriminator (D).
The input to G might vary based on your current setup. One option is to feed in random noise vectors and let G generate fake images using transposed convolutions. You could also feed in other images and learn to transform these images, but let’s stick to the DCGAN example here.
D on the other side is often a model which might be used in a classification setup, i.e. it gets images as input and tries to classify fake and real images.
Back to your original question: you might try to visualize the input tensor to G in relation to G’s output, if I understand your use case correctly. Even though you are randomly sampling the input, you’ll see that the output is smoothly generated, if you use a reasonable interpolation method, which means that certain “areas” of your multidomensional gaussian create certain features in the images. I’m not sure, if t-SNE is the best method to do this, so let’s wait for other people to give some feedback on this. 
I guess you’ll