Which would the manufacturers most prefer that we use?
Not sure I understand what you mean here.
For that matter, have the manufacturers manufactured anything yet?
No, they will most probably manufacturer on demand. But they always have the option to stock popular boards to increase their margin.
It seems what's novel (and promising) here is having a place where people can easily buy something and then automagically get the physical thing delivered to them, already assembled. Am I right?
Yes, it is very easy to order a pcb (or assembled board where available) on the site. Especially for none electronics people. Without having to bother with weird file formats, layers and other cryptic stuff.
If people just want the files or PCB's and then take it from there, there are already commonly existing ways to do that, like posting them in a zipped file on a thread somewhere or on github.
Absolutely, everyone is free to manufacturer things anywhere. I don't care. But it's a nice gesture to support the author (they get a small kickback) when placing their order on openhardware.io.
Anyhow, it's upp to the author to activate the sales function (by creating a revision under the sales-tab). Nothing gets activated automatically. Or if the author has the time, they can handles sales themselves, on ebay, just by adding the link in the sales tab (we fetch the price automatically and present it on openhardware.io).