It REALLY isn't. It is simple simple simple code.
It's rediculously simple.

Works perfectly for me in IE5, IE6, Opera, Firefox, and IE7, so I fail to see who it is at all picky in logging out.

If you don't click Remember Me, it won't plant a cookie on your browser, and so, when you close the browser, it can't identify you and automatically log you in - just like any website.

Every browser session is given a unique id by php, which is used to reference store some information about your login status, and what account you are using.


EDIT:
I a**umed you mean't the logout was buggy. I am unsure now.

Regardless of this, I'll explain how some of this stuff works...


When you log into the game, the server hands you a session id(like most sites do).
This session will expire after a set timeout - I believe php's default is roughly 20 minutes.

Once your session has expired, a new one must be created - if you clicked Remember Me, the game will automatically link your account to the new session(meaning, you log in).
However, if there is no cookie, it won't be able to, and you will be regarded as logged out by the game.

To log in manually, you enter your username and pa**word, which the game uses to find your account, and validate that it is yours.
It then links it to the session, which is used to remember what account you are using.

On top of all of this, your player account also has an expire time of 15 minutes.
If you aren't visiting the game for more than 15 minutes, the game cla**es your account as offline.