As a part 121 flight crew member, it is great to hear examples like this. We train for this very scenario in every recurrent simlator session.
One thing that we're trained, which you can hear in this clip, is in an engine failure event, landing right away isn't necessary. ATC might get a little excited and start clearing you to do everything. But my company trains us to do exactly what this crew did: Tell ATC that we've got a problem, tell them what we're gonna do, and tell them to stand-by. That gets them out of our hair for a couple seconds while we examine the sitation.
Flying around single engine isn't something that we need to land right away for. Take a few minutes, read the checklists, configure the aircraft for single engine flight, and talk over what you're going to do. In some cases, it is not a good idea to land at the airport you just left. There may be better options out there (LGA-->JFK/EWR, DCA--->IAD, MDW--->ORD)
Kudos to this crew. Handled it very safely and professionally