[WannabeArtist]

Well, this *should* be pretty easy. Just do a session_start() at the beginning of your game's php script and match the session_id() with the session data in your forum's database.
I can only tell you how that should work on vB 3.0 as I don't have 2.3.3 set up.

<? php
session_start();
require('path_to_forum/includes/config.php');
mysql_connect($servername, $dbusername, $dbpassword);
mysql_select_db($dbname);
$userdata=mysql_query("SELECT * FROM session LEFT JOIN user ON(session.userid=user.userid) WHERE sessionhash='".session_id."'");
if ($userdata=mysql_fetch_array($userdata)) {
    your game's php code where $userdata got all the info stored in an array
} else {
    display login box
}
?>

Well, as long as your users go to the forum first and only after that to the ok, this should work. However, if they close all their browser windows and then go to that site it probably won't recognize them. Hope I was able to help out a bit, and good luck.

BTW, I *think* that simply including the global.php file of the forum does all of this and more automatically. If I'm able to remember correctly the data would be accessed through the array $bbuserinfo