"All of the current 11 judges, who serve seven-year terms, were appointed to the special court by Chief Justice John G. Roberts Jr. ..."
So they're asking the Supreme Court to stop the spying program facilitated by the secret court, which is staffed by the Chief Justice of the Supreme Court.
Staffing the court is apparently part of his duty as Chief Justice, and as such does pose a conflict of interest with this case. Carrying out his job does not imply any point of view regarding the constitutionality or ethics of the spying program. He doesn't get to refuse to appoint judges as the law requires whatever his opinion. He only gets to judge things that are officially challenged in his court, and even then only after reviewing evidence and arguments from both sides.
Just doing his job, right? Are you seriously trying to imply that the Chief Justice of the Supreme Court, literally THE authority on interpreting the Constitution, as an American, has no connections and is powerless to influence the world in any way outside of the court cases placed before him? Think of it this way - if he felt what he was being asked to do was a violation of the Constitution, wouldn't his participation make him a co-conspirator to that crime?
So they're asking the Supreme Court to stop the spying program facilitated by the secret court, which is staffed by the Chief Justice of the Supreme Court.