How is the Journal for an Annual Review Chosen
Short version: it's a money issue, at least in the case of Review of Particle Physics.

Disclaimer: I'm not part of the particle physics community, so I might get some details wrong in the following, but I think the broad strokes will nevertheless be correct.

First of all, I think the scale of what the Particle Data Group is doing shouldn't be underestimated. They are a group of more than 200 contributors, who publish a humongous, ever growing biennial authoritative and extremely well-regarded review article. With over 2,000 citations per year, I think it's fair of you to say that the article would boost most journals, rather than the other way around. Obviously just the data collection, editing, and fact checking requires a fair amount of funding.

Now, the crux of the matter is that they (PDG) also distribute the article in the form of a book, and a shorter (200-300 pages) booklet for free. We're not talking small numbers either - more than 30,000 copies of the booklet, and over 10,000 copies of the book (see e.g. this APS announcement).

As I understand it, there is a process where different publishers bid on the right to publish the review by offering to shoulder (at least) part of the cost of printing the books. (CERN covers at least some of the cost for the booklet.) This is the main reason why the article has moved around between different high-energy journals. Then in 2014, apparently only Chinese Physics put in a bid, and consequently went on to publish the article.