For example:
Logging out all sessions lets you post from devices that were once logged in. I clicked the logout all button from my laptop and my phone can still post to the forum despite saying sign up/log in at the top. Don't know if it's possible to access your games still with a manual URL. Haven't really experimented.

Basically you should probably log out manually from all you sessions rather than use the close all sessions button.

[EDIT] And yes, I posted this without being logged in.

The forum haven't really been fully updated to the log-in system the rest of the site uses (or, for that matter, to the same mobile-friendly layout). I'd imagine the "logout all sessions" logs out the new way (which shows in the top navigation bar, even on the forum), but the old way which the forum actually uses isn't touched.