The defender doesn't take damage unless the attacking creature has trample. This is because the attacking creature is still "blocked" and so must assign its combat damage to its blockers, of which there are none. The relevant rules are as follows:
509.1h An attacking creature with one or more creatures declared as blockers for it becomes a blocked creature; one with no creatures declared as blockers for it becomes an unblocked creature. This remains unchanged until the creature is removed from combat, an effect says that it becomes blocked or unblocked, or the combat phase ends, whichever comes first. A creature remains blocked even if all the creatures blocking it are removed from combat.
510.1c A blocked creature assigns its combat damage to the creatures blocking it. If no creatures are currently blocking it (if, for example, they were destroyed or removed from combat), it assigns no combat damage.
702.19c If an attacking creature with trample is blocked, but there are no creatures blocking it when damage is assigned, all its damage is assigned to the player or planeswalker it's attacking.
