Regardless of the reason concerning the controller's issue, the aircraft were never in any danger, or shouldn't have been. There are procedures in place for all types of contingencies and emergencies. Communication failures, although rare do occure. I'm sure that the pilots followed the correct procedures resulting in a safe approach and landing.
I've flown for 40 years, and have had my share of "Oh, S**T !!" moments................ but, I'm still here and have never dinged a plane. I doubt the pilots considered this an emergency, but, I'd bet they were thinking WTF ??