by Artaterxes
It's called the "concurrent attack rule." Each round, the cards that you draw for your units are all resolved, regardless of what happens to those units that round. The fact that your warriors got routed AFTER they drew cards doesn't change that you still have 2 routs and 2 damage to deal.Your opponent would assign the 2 routs however he likes (to undamaged units if possible). Later in the round, your opponent would assign the 2 damage however he likes, but he must damage a previously damaged unit, if possible. If the dragon was already wounded, and 2 more damage would kill it, then yes your opponent would be forced to kill it.
Scott is correct assuming the dragon is undamaged.