I don't see any airport there. Just a tiny village at the northeast corner.
It doesn't look like the topography would be very favorable to constructing an airport.
I think that’s why he needed a simulator — to practice landing on topography like that or on a short strip of asphalt road or in a crabrun on the beach or in the waters just offshore.
The first investigators must have suspected this or gotten a heads-up from his computer — note their yellow NTSB flight path. It ends up right at New Amsterdam — right on the last Inmarsat arc:
https://www.facebook.com/178566888854999/photos/pcb.740971779281171/740971732614509/?type=1&theater
And IIRC early on there was a significant air and sea search of the waters right there.
He may not have made it but it doesn’t mean that he didn’t try — that is, if that is the island in his computer.