Speedbird clearly stated an emergency with Mayday Mayday Mayday, and it was understood by ATC. Since they where coming back for a 3 engine MLW landing the airport had ARFF out. ATC did clear the airspace and runway for Speedbird. ATC will most likely not downgrade a Mayday in such a situation, why should they? ATC knows that the pilots have a very high workload in this situation, so they do not go in semantics. What need to be done was clear and ATC helped as much as they could. Communicate comes always third for the pilots
Bear in mind they will have been communicating to multiple ATC agencies. It sounded very well managed to me. Compare also this (certainly the video is better...)