Koushik Dutta didn't add a new quick settings tile. The "Cast Screen"-Tile is implemented by the android system and appears sometimes. It's a shortcut to the "cast screen"-menu in system settings. Koush added new options for this menu (i don't know if there's an open api or if he needs the root permission for that) and now, the tile is always displayed because there's always content.
To answer your question: No, without system modifications with root, you can't add tiles to the android quick settings. (Edit: I haven't read that you'd also use root. So, you can't add tiles easily and the mirror application by Koushik Dutta doesn't do that, too.)
PS: It isn't because of CyanogenMod, because I use stock android and the app works, too.
Update 2019-08-08: With Android N, there's an official API to add custom quick setting tiles (see Sam's answer).