You're right, insofar as "bird" is not jargon, or in 1:1 correspondence with jargon, in any scientific discipline. There's just theropods, some of which happened to survive, where people call the descendant species of those particular theropod species birds. There's no rule specifying whether those theropod species themselves are birds, or whether species that are 99% like them but happened to die off due to pure bad luck are birds, etc.—because we don't need such a rule for anything.

If we did, though—if "bird" was jargon under some branch of science, the way that "fruit" is jargon in culinary science†—then I would guess that the criterion for it would be something like "a theropod with adaptations that would make it likely to survive the K-T extinction, all else being equal", making both the ancestor theropods to current birds qualify, as well as the bird in the article. But, well, nobody needs that definition for anything, so it can't really be argued what the definition "really is."

† https://en.wikipedia.org/wiki/List_of_culinary_fruits