DFC
You quote the pilot on the video who rightly called a Mayday. He and I are both commercial pilots who fly regularly and practice single-engine approaches and go-arounds every six months. The difference is that he had a catastrophic engine failure on departure, probably with a full pax load, which should always be a mayday on a twin unless you are perf A and very light. I had an engine stop producing thrust, at 4000 feet on 10 nm final for a decent length runway with two qualified pilots on board (a single-crew aircraft). Once I established that I could make the runway I did not "require immediate assistance", apart from the priority given anyway to a pan.