Interesting article! I flew DTW-PEK and back last April and was wondering about the special additional requirements that airlines must meet to operate these flights. The referenced article covers all of that.
Our "westbound" flight was straight north from DTW over Hudson Bay to the North Pole (almost -- 89.2 deg. N), then a slight left turn, and straight south over Lake Baykal in western Siberia, Ulanbatar in Mongolia, and finally a little jog east to PEK. This would be Polar 2 according to the article.
The eastbound (returning) flight took a more southerly route along the coast of Siberia, over the Bering Sea and Alaska.
"In God we trust, everyone else bring data"