Is it legal to publish (in a book) an online dialogue without the permission of all participants?

The answer is "it depends." In the case of the material at this web site, there are copyright issues covered by the site owner's terms and conditions. If the portion of the dialog you are copying is relatively small compared with the whole, it is possible that you might rely on the doctrine of "fair use" in doing the copying. The availability of a fair-use defense is always fact-dependent and cannot be assumed as a matter of course.