Latest discussions are just kind of digest from all the forum, so if user is not logged in, he still is able to browse forum-by-forum to see the new stuff? Honestly I don't understand such approach. And it would be useful only if you are set up $statsPageModern setting to FALSE which is kind of old-fashioned layout...
Anyway, the simplest solution in this case is only to modify index.php. Where it says
you need to put a condition
$listTopics='HTML code for guests';