As far as I can see from the article the "birds" were of the ostrich kind, not the flying kind we imagine when hearing the word "bird". As far as I know the modern science also says that many dinosaurs that didn't fly also had feathers. So why aren't the other dinosaurs considered "elephant birds" while this creature is?
Because even though it's all a continuum, this animal was much closer to modern birds than to dinosaurs based on the various ways these things are classified. For one, it didn't have a dinosaur style jaw and teeth but a bird beak. Where to draw the line isn't easy, it's fuzzy, but I don't think this case is fuzzy. These were birds by every way we discuss what that means today (which never requires flight).
I might try to explain this but I think I will definitely miss something or won't be able to articulate. Instead, I would suggest episode 1 of Life of Birds [1].
David Attenborough talks about the evolution of birds, what classifies a bird, where do we draw the line between dinosaurs and birds (he even talks about this elephant bird) in the first episode of Life of Birds [1]. Also, watch the whole documentary if you're interested.
It is legacy like many things in zoology like taxonomy. They were thought to be more like giant lizards than birds for a long while even if they couldn't ignore the most obvious convergences. It isn't limited just to ones we know about only through paleontology. There is even a civet genus labeled 'paradoxus' that eats mostly berries and fruit despite being under the carnivora family.
The Aristotelian taxonomy was even worse with things like considering beaver a type of fish and poultry as distinct from meat because meat is land animals.
Common names are even worse for it which is why the current lineial system exists in the first place like all of the different names for mountain lion. Taxonomy isn't objective science in itself (although it should be based off of it to be of any use) but it is very useful to science.
Technically we can reindex the taxonomy and rename any time but it would be such a pain to keep track with multiple systems old and new and all of the controversies that it probably wouldn't be worth it until our understand diverges enough that it loses all meaningfulness.
For instance the classical elements of various systems were discarded completely as useless even as an additional layered category. Fire is a state of matter, earth is actually composed of many of the table of elements even more if we don't have metal separate, water is composed of two different elements that appear elsewhere in both air and earth. And the old associations like gold with fire and sun? Completely unfounded. Thus it is pretty much useless as a tool for improving our understanding and limited to a motif.
Meanwhile even if DNA testing shows that the line of descent doesn't match up at all reliably with parallel evolution the organization could still be good for rough body shape for instance. Even if to give a counterfactual and deliberately absurd example it later turns out that humans actually evolved directly from an extinct strain of whale filing humanity among apes is still informative in morphology and not wrong in that sense even if the descent aspect was shockingly discreditted.
