I think all his maps are just in the exact same projection. That's suitable for mapping regions of a continent, but it may not be ideal for a whole world. (It might be OK if you don't want regional maps of the poles.)

LAEA is good close to the projection centre, distortion being about 2% within 15 degrees, 5% within 30 degrees, and 10% within 45 degrees. The further out one gets, the more squashed the map becomes; by the time you reach 90 degrees (half the planet) it's up at 25%, equivalent to turning a square into the shape of a widescreen TV.