Is the process for publishing a multi-book review essay (i.e., the kind you often find in World Politics and other journals that allow this type of exposition) similar to publishing a regular article? That is, does one collect the books, write up the essay, submit it to the journal for review?
Or, are these things typically commissioned by the editorial board/chief editor, either unsolicited or after solicitation by the author?
It depends on the journal. Many ask you to contact them first with a sketch of the proposal. Procedures otherwise vary widely, particularly with respect to peer review. The best way to find out is to look at the journal guidelines and/or contact editors.
^^
Historically, it has helped at World Politics to have connections to Princeton.
Mr. Slippery is right. Approach the editor with a proposal. More often than not they will be pleasantly surprised to hear from you -- they waste a lot of time trying to find people to do things (and get a lot of negative replies). So if it is timely and well conceived, you have a decent chance at taking this forward. If you are thinking WP your aim is high, and that's mostly an in-house operation, but there is no downside to inquiring.