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.

What do you hope to achieve by contacting his current institution, which does not have any skin in this dispute? As you describe it, this person is doing well at his current place of employment so it seems unlikely admin there would get involved.

Somehow, I cannot imagine that the police would treat this with significant priority now.

A better alternative might be to work through the publisher. I presume this publisher may have formal or informal communication channels with other publishers, and thus might be able to organize some sort of pressure campaign through collective action (v.g ban on publication of papers by this person, or this person is not allowed on editorial boards of journals, etc).