While they may have shut the wrong engine down, the problem is that they did not deploy flaps, which do not require hydraulic power to deploy.
Coming in at flaps-up speed was suicidal. They also “floated” down the runway and used up over 3000 feet of the 10,000 foot runway before touching down.
They hit a reinforced concrete wall at over 150 mph. If that barrier was not there, they would have gone through the airport block wall, but more passengers would have survived.
“was suicidal”
I’m surprised this possibility has not been raised.