Yes, it's abuse of process, and it's a swindle on the taxpayers. While preemptive Doe suits are not per se frivolous, if one has some reason to believe that a specific unknown person is likely to harm one, they are not an excuse to treat the Article III federal courts as a sort of free mall cop at the taxpayer's expense.
Otherwise, any business, such as a mall, could simply file a preemptive lawsuit against Doe shoplifters, alleging that every store in the country gets shoplifted from at some point, so the state or the feds should step in and provide them free security. For that matter, any company about to release an album could file a Doe suit against a few hundred million Does, demanding an injunction against well, everyone in the United States. They could file a suit against everyone in the United States enjoining them from pirating albums they haven't even decided to release. After all, certainly they will release albums in the future.
This lawsuit is also unconstitutional. The Article III federal courts, as has been pointed out, only exist to decide actual cases or controversies, not imaginary ones. Then there's due process. Nobody has been served with this imaginary lawsuit. So the injunction is meaningless, since nobody had any notice of it. Then, the injunction also violates separation of powers. Article III courts aren't law enforcement, there to patrol for possible future violations of the law. They don't have jurisdiction to act as free mall cops for businesses who fear that some unknown person, in the future, will commit a shoplifting offense.
And to come back to the original point, it's an abuse of process: that is, the use of a lawsuit to obtain an improper collateral advantage. They're suing unknown people for precrime, in order to get free mall cop services from an Article III court, at the taxpayer's expense. Unfortunately, abuse of process is usually pursued by people on the other side, who allege their rights have been violated by the abuse of process. Since these crooks are only ripping off the taxpayer, nobody would have standing to challenge their thievery.
This lawsuit should be dismissed sua sponte (by the court on its own motion), with prejudice so that they can't even file it again in the future, as a sanction. The lawyers (and I'm using that term loosely) should be sanctioned under Rule 11 and reported to their state bar associations. Since we're talking about fantasyland here, they and their clients should also be slowly boiled in oil, while bootleggers videotape their thrashing and screaming for immediate distribution over the Internet via streaming video.
Since we're living in reality, they'll probably be given a profile in the ABA Journal for innovative new legal strategy, and make partner in record time.