Professor takes our money and goes incommunicado, do we complain to the department or the police?
Obligatory disclaimer: I am not a lawyer...

This sounds like a contract dispute: whether the editor has discharged his side of the agreement. As such it is likely to be a civil matter rather than a criminal one. I very much doubt the police will be interested in pursuing anything. In general terms, the legal recourse would be to sue the editor in the civil courts. I suspect that the costs of doing so outweigh the benefits.

Could you report it to the editor's university? Yes. However, it isn't clear what this would achieve. As @ZeroTheHero says, they (apparently) have no involvement in the dispute so far. From their perspective it will be your word against the editor's; even if they wanted to resolve the dispute, it is not clear how they would go about doing so.