I would agree with EtOPS that a shallow climb all the way upto a safe altitude would be a must prior to turning. However, being that I fly a senecca all the time I would not recommend a single engine go around feathered por not, especially with 5 people on board. That aircraft was probably pretty close to gross wt. What is a huge factor missing is what was the density altitude. If it was a hot day then we can expect relly bad performance.
As to why would he go around. That would be second guessing, but I would rather belly up down a runway into the grass and even knock into a fence/trees at the end of the runway at 10kts than try and climb in one of them. Yes you can, and I simulate feather for my students during a Single engine ILS and make them Go-around from the DH. If they don't clean up quickly that rate of decent doesn't reduce much. I think the left turn if intentional may have been a bad idea as you further lose climb performance due to increased Drag. What I see a lot of here in the US is that people own there own plane and fly around 10years, but when do you think was the last time they practiced a lot of engine failures. I see this when I give people the required two year flight review.
Beagle, most light twins lose about 80% of its climb performance when they lose an engine. The senecca is 83%. The FAA only requires aircrafts over 6000lbs to have a single engine climb performance. It is published in the POH on seperate tables what the multi and single engine performance should be at different altitudes.