Their joking excuse in that video clip was the warm winds and ocean currents did it, so same stuff that causes western Europe to be warmer than the parts of North America that are the same distance or even closer to the equator. I don't know enough about this stuff myself but I'm pretty sure that that alone wouldn't be good enough to explain away a proper cold south pole if they intended Azeroth to function like earth (seasonally) which it does seem to since we also have a harvest festival and winter holiday that involves snow. I think they just didn't really think about it and there is no real explanation so in the end what matters is if Blizz decides to retcon it or not and it could go either way. Right now there is no cold southern pole, but if they decide to make one, it would retcon all the maps/lore but not their established climate.