How to Deny Access to No Referrer Requests on Multiste with Mapped domains

You could hook intop pre_comment_on_post:

add_action( 'pre_comment_on_post', function(){
    if ( empty ( $_SERVER['HTTP_REFERER'] ) )
        exit;
});

But … be aware, not all requests without an referer are actually spam posts. Some firewalls and proxies strip this field. And most automated spam comes with a Referer field filled with the name of the spammed domain. So you will get many false positives.