There are 4 primary Polar routes that go close to the North Pole.

Polar 1 & 2 aimed at traffic North America - China/India
Polar 3 & 4 for North America - Japan/Korea

The Russians charge hefty fees for their usage, which currently goes into Aeroflot's pocket.

So going east from HKG flying along the East coast of Japan to the Aleutians, across Alaska then Northern Canada often makes good economic sense and why this route is preferred for HKG-East Coast traffic. It also follows the Jetstream which operates 50-60 degrees latitude and not over Polar Regions.

Return from NYC is more difficult because Northern Hemisphere winds flow clockwise, though I have (rarely) flown westbound from the East Coast. The choices are simply flying Polar over Siberia or entering Russia further West.

This alternative non-Polar Eastbound route can go East of Greenland, above North Cape, over Novaya Zemlya, across Russia to flow into Chinese airspace in Xinjiang province. Again this hits the Jetstream south of Novaya Zemlya.

Deciding which point to enter Russia is often dependent upon storms which are stronger in the Russian/Atlantic Arctic than the Canadian Arctic, especially in Winter.