To understand news in the world of biology, one needs sufficient context. While evolution is a popular conversation topic in life science, an equally important topic is the ecosystem. Studying ecosystems has revealed the vast interrelatedness of life. As the author of the first link explains:
"From high-flying atmospheric bacteria with heretofore 'unknown' DNA to crustaceans living in caustic sulfur environments in the deep blue sea, not one bit of life on this planet is not related and interdependent."(FYI: The "heretofore 'unknown' DNA" quip is a reference to another recent piece of biological news regarding the question of life's beginning.)
This is why the extinction of a single species (or the addition of a single non-native species) has the potential to be cataclysmic to its ecosystem. Earth can be described as a single ecosystem, and the human organism is an essential part of this ecoystem. Thus, the loss of any species has a profound effect on us, whether or not we are aware of that effect.
How does the loss of a bird species effect us? Here is one way: Humans will always be striving to understand their neurological machinery, and comparative animal studies occasionally provide profound insights into how minds, in general, work. Bird brains are extraordinarily complex for the animal kingdom, and I think they might be able to teach humans a lot--specifically the way in which brains, in general, learn. Every time we lose a species we lose a potentially revelatory example.