So, if I'm reading this right, Quad9 is just a recursive dns resolver here. Why are they being enjoined rather than whoever runs the authoritative server?
Because when you see it from Sony's perspective, Quad9 is a provider/tool that allows people to circumvent restrictions / legal decisions to block the website.
More importantly unlike other DNS providers (like the root servers) it censors the domain names that it will resolve, Sony's argument is that because it chooses some domains it should censor the ones that it wants too