I'm really loving these videos, well done. This is false. Sword of Islam and The Republic only unlock the appropriate group so that the player can play them (Muslims and merchant republics respectively). The gameplay features were added in patches that were released at the same time as the DLC. The same mostly goes for The Old Gods except that it also includes the 867 start date. There is no must-have DLC for CK2, although the complete collection is so cheap right now that you might as well get it + the Old Gods and any other of the new DLC that isn't included that tickles your fancy.