The reason why I thought it might be an issue, is that according to Wikipedia, The 777-200LR is the world's longest-range airliner and can fly more than halfway around the globe; it holds the record for the longest distance flown non-stop by a commercial aircraft. . It hadn't occurred to me that because the 777 is a twin engine, it can't really use all that range. It needs to stay near airports.
Twin engine planes absolutely can cross oceans -- if you need three hours' flying distance in the worst case (ETOPS-180), then you can cross up to six hours of water between any two backup airports. North Atlantic routes have only a few hours of contiguous water between, say, Greenland and Iceland. Even the Pacific has enough small islands (e.g. Hawaii) to make something like this possible (shaded areas are outside 3-hour range):
