Thanks for pointing out exactly what you're looking for. That 'menu' up there is actually the SCLogin module. It's not a Joomla menu that we're showing there. The way we have it configured is:
* Text links for Login / Register are done by setting the "Modal Style" option to "Text" in the SCLogin module.
* Then we're enabling the Show User Menu option to show the My Account menu from Joomla to the users.
** To make the User Menu a text drop down like that, there's one modification you have to make to the /modules/mod_sclogin/helper.php file. Around line 377, you'll see:
//$menuNav .= '<ul class="menu nav"><li class="dropdown"><span>'.$parentTitle.'</span>';
$menuNav .= '<ul class="menu nav"><li><span>' . $parentTitle . '</span>';
//$menuNav .= '<ul class="dropdown-menu">';
$menuNav .= '<ul class="flat-list">';
Uncomment (remove the //) the 1st and 3rd lines and comment (add a //) to the 2nd and 4th lines. That will switch it to a text link menu. However, you may needs some additional template styles to make that work well with your template (which is why we don't have an option for that mode yet).
The other option is to only show the SCLogin module to guests and then show a registered mod_menu to logged in users.
I hope that helps,
Alex