As they mention in the article, it is known that dream imagery does invoke responses in the visual cortices (i believe even in V1), however the responses are weak in the early cortices, so it's not currently possible to "read" the dream imagery (i assume they would have done it if possible).
I am not sure how well the algorithm would work without the V1 activation, since V1 is retinotopically organized, making it quite easy to decode.
So V1 is 'raw' and later cortices have performed more processing on the data causing it to be higher level, which in turn makes it harder to translate it back to a visual?
Yes that's more or less the picture. The extraction of images from V1 has been performed before, the novelty in this paper is that they reconstruct motion too. In the case of dreams, the flow of information is in the reverse, higher level areas projecting to lower level, creating the illusion of vision. It's not yet known if an actual image is formed in low level virtual cortices from dreams.
Reconstruction of what the subjects are currently looking at is interesting but a direct window into the imagination would be something else.