It's hard to have a good intuition for great circle routes. The shortest path between those cities does in fact go all the way up to Alaska, crossing through the Aleutians:

http://www.gcmap.com/mapui?P=YNT-LZC

Adak is about as far south as the Aleutians get, so it makes sense that the ship would have passed (relatively) near there.

This counterintuitive bit of geography is why Anchorage has one of the busiest cargo airports in the world, despite its small population.