That's just the thing, though: Liao had all the time in the world to think about it. There was no imminent danger, until he created it. Losing an engine on takeoff is a bona fide emergency, but the only immediate actions you need to take are to keep the airplane straight and keep your speed up. For everything else, you can take your time and analyze.

Sully, on the other hand, had a minute or two before he was going to run out of altitude, no matter what he did. Every moment counted there, in a way that it definitely didn't count in the Taipei crash (until the pilot made it that way).

This attitude is mistaken. Sullenberger had no good choices and was going to crash, his scenario was far more dire.

The Taipei flight had a perfectly fine engine and there is no reason for any of this to happen. The plane could fly just fine with one engine out.

That was my observation as well, the two incidents were completely different, loss of one engine at take off, and loss of both engines a little further into flight. IMO the author commits a disservice to the Asian pilot for not making this explicit.