A330-300 S/E G/A Goose Bay
 

A couple of weeks ago a Delta A330 en-route to Amsterdam experienced "engine performance issues" in one engine whilst over the Atlantic NE of Goose Bay. Whilst it was diverting to Detroit, however, the issues worsened and the crew decided to land at Goose Bay. After having been cleared to land and on short final at around 1200' the problematic engine failed and a go-around was flown to a landing on the reciprocal runway. My question: at such a late stage of the approach, would it not have been safer to land instead of flying a single engined go-around at an unfamiliar airport with all that entails? Surely the crew must have discussed the possibility of the suspect engine failing and they would have performed any necessary S/E approach and landing calculations beforehand?

Many possibilities, and I've no Airbus knowledge, so these are general comments.
It depends on what the engine problems were. If they thought they could return to Detroit, but then decided to land much earlier, that would suggest they knew they had a substantial problem, but not yet a total failure. Some would have planned the whole approach and landing as an engine-out manoeuvre. Others, as you suggest, might use both but brief & plan for the worse. (If they were operating the problem engine at reduced thrust and then idle during descent, perhaps they thought it was more robust that it proved.)
Some airlines have an SOP of GA if an engine failure on finals below XYZ feet. Others allow captain's discretion to continue. If the former, then planning and executing the approach as an engine-out, even if only at idle, would remove that possibility: i.e. no surprises. One wonders what their ELW was. That could have led them to hope for 2 engines.
What happens on an A330 if you fly as if SE, but one is at idle? Does that confuse all the computers and cause more problems?

I'd be more curious about the runway change.

They are lucky because the FARs do not take into account a landing climb SE! Below the MAP SE is not required to be accounted for. Perhaps they(DL) paid for more data I don't know

Unlike other twin engine Airbus types, the 330 doesn't have a PTU. If you lose an engine, you lose a hydraulic system and a landing distance correction applies.