In case someone bumps here again, I found two ways it can be achieved within a theme without using any using module.
Using custom CSS:
.user-logged-in .menu.menu--account a[href="/user/register"] { display: none; }
Using custom JS:
$('.user-logged-in').find('.menu.menu--account a[href="/user/register"]').hide();
This is applicable only if you are customizing your theme in any way.
