$action = $_REQUEST['action'];
$Responder_ID = $_REQUEST['r_ID'];
$Search_EmailAddress = $_REQUEST['email_addy'];
$Subscriber_ID = $_REQUEST['sub_ID'];
It's a combination of hacked-in register_globals(), with a measure of short-to-long name conversion. It's like he thinks he's going to run out of space in the URL.
Oh, and the really fun part? $_REQUEST is already global. So it's adding an extra step to rename them, and then everywhere you pass it into a function you have to remember to global it again.