Listen to it again. The stress in the controller's and the pilot's voices is clearly evident. They both did a great job, and it's impossible for most humans to completely suppress all signs of the stress we'd all face in such an instance.

As mentioned, the pilot got his own callsign mixed up and his final transmissions were very terse - the last one was rapid-fire compared to the initial calls.
All this is completely understandable - you'd have to be clinically dead not to react in such fashion. It also suggests the flight crew was very busy doing the priority items within the cockpit - adhering to that tired yet relevant maxim: Aviate, Navigate, Communicate. In that order.