These galaxies are at some in-between stage where all the dust isn't gone, but "reddens" the quasar light. This hypothesis is bolstered by the discovery from the quasar spectra that the material is moving rapidly and in all directions, signs of a massive outflow.
All this information comes from tiny points of light like the red dot in the image above. Well, okay, it's a little more complicated than that. The spectra of the quasar is used for a lot of this work, that is, the light is spread out by wavelength not unlike a rainbow. Only, this is an infrared rainbow and it helps astronomers piece together the types of gas present in the galaxy, where outflows are present, and that so much dust is present. Particularly, the astronomers compared the data to models of quasars to find a description that best fit what they were seeing.
From just a tiny point of light we can learn so much about the universe's history, and thus, our own history as well. I think that is pretty amazing stuff.
Image Credit: Infrared colour image of ULASJ1234+0907. From Banerji et al. 2012, MNRAS. Created using data from UKIDSS and WISE.