This is one of those cases of biology terminology that really makes me groan, because although it can be a useful designation, the word choice is just... not excellent.
Cells interact with each other all the time, particularly in a multicellular organism: it's absolutely essential that they do. That means that one cell type can influence the behavior of another cell type.
When you describe some mutation as "cell-autonomous", you're basically saying that the phenotype is just dependent on the cell where the mutation is expressed. For an example off the top of my head, a mutation in a pigment-producing enzyme causing albinism is almost certainly going to be cell-autonomous: if you introduced the mutation in only the pigment-producing cells, you'd get exactly the same result as if the entire organism had the mutation. You could understand what is going on if you just cultured some of those cells in a dish and compared those with and without the mutation. You don't need the whole organism to understand what's going on, just the autonomous cells in a dish.
You ask about non-autonomous, though. Again, I think it's easier to use some example. Searching Google scholar for "non cell autonomous" one of the first results is this paper:
Di Giorgio, F. P., Carrasco, M. A., Siao, M. C., Maniatis, T., & Eggan, K. (2007). Non–cell autonomous effect of glia on motor neurons in an embryonic stem cell–based ALS model. Nature neuroscience, 10(5), 608-614.
They're looking at mechanisms of amyotrophic lateral sclerosis (ALS). ALS is a neurodegenerative disorder: the overall phenotype is that neurons die. However, this paper isn't about neurons, it's about glia. When you co-culture neurons and glia, you're looking at the neurons for the phenotype (do the neurons die?), but it's the glia where the genetic manipulation matters. This particular paper is about SOD1, which is involved in protection from oxidative stress.
Back to your paper, this is talking about neuronal guidance cues that are important in the developing nervous system. Simplifying a bit, typically neurons express some collection of receptors for various guidance cues, and other cell types present these cues on their cell surface or excrete soluble molecules. Growing neurites then follow the concentration gradients (either in an attractant or repellant fashion) to get where they belong. Dcc is also called the netrin receptor. The authors describe mutations in Dcc as being cell autonomous for neuronal migration, because you only need the mutation in the neurons to see the phenotype. This makes sense mechanistically because it's a receptor expressed by the neurons themselves.
However, if you had a gene of interest involved in netrin-1 synthesis or expression, that would possibly demonstrate a cell non-autonomous phenotype: it doesn't matter if you interfere with netrin-1 expression in the neurons themselves; as long as their receptor and signaling pathway is intact, they'll navigate just fine. However, if you put normal, unmutated neurons into a nervous system where all the other cells fail to express netrin-1, even those wild-type neurons won't know where to go. The phenotype: failed migration, is occurring in a different cell type than the ones that need to be genetically altered for the organism to show the phenotype.