Is this article self-contradictory, or am I missing something?
There's no contradiction. Firn is an intermediate form between snow and ice, with a density between that of snow and ice.

The frozen fluffy stuff that falls from the sky -- that's not ice, it's not firn. It's snow. It's also not very dense, typically less than 0.5 grams/cm3. As the snow sits and gets compressed by snow atop it, some of the gas gets squeezed out. The snow changes from ice to firn. The authors are using density between 0.55 and 0.82 grams/cm3 as the definition of firn. As the firn sits even longer, it changes from firn to ice. Note that solid frozen water (no air pockets whatsoever) has a density of about 0.934 grams/cm3. Compressed former snow with a density of 0.82 or higher acts a lot like ice. It is ice, not firn.