Prions evolving are significant because they are, in essence, only malfunctioning proteins. But they reproduce by finding other proteins of the same gene and causing them to malfunction as well. That is all they do. By destroying one type of protein like that, you don't have it anymore and get sick (and die).
What is amazing is that if they are evolving and changing protein targets, we now have a mechanism that they can sustain themselves in populations for the long term and be a tree of "life" of their own. They aren't just malfunctioning proteins, they are disease vectors that change to continue to infect.
The function of DNA isn't really different, it functions as the genetic material in prokaryotes and eukaryotes. The packaging of the DNA is different, as are the evolutionary pressures due to population structures.