I finally found an application for which that menu item does something.
With Coda 2, a text editor for web developers, when I click on "Show Recents":
The screen dims, as it happens when using the Dashboard
The windows shown in the screen disappear
An icon for each of the most recently open files for that application appears
I am now using OS X 10.8.2; it could be that something has been fixed inbetween the while, butmoment I asked this question and the moment I answered it. I still don't see anything with Messages, and Contacts. The only difference seems that now the Finder window doesn't appear anymore, not even for applications without recently open files.
As side note, this menu item seems to be shown when "Show All Windows" is not shown; for an open application, "Show Recents" is always replaced with "Show All Windows."
I guess that happens because an application normally shows a list of recently open files in its dock menu, when active.
Now, I wish the applications would be able to say to the OS if the "Show Recent" menu item does make sense for them. An application that usually opens a specific hardcoded file (and only that) should not show that menu item.