The new finding is that that individual dino appeared to be hatching in the same way present day birds do. (As opposed to for example how crocodiles do.)
The article states that this behaviour was not previously observed in dinosaur fosils therefore it was not known which way they hatched exactly.
So, it was preparing to hatch like a bird, unlike other dinosaur embryos found before.
In phylogenetic taxonomy: (1) that's exactly what it means, and (2) that's why Aves is within Dinosauria.
EDIT: I guess they're within a clade Avialae that is nested under Dinosauria. So yes, it looks like you are right.
Doesn't the term "avian dinosaur" in some sense mean "survived K-Pg"?
(I edited my original comment to be more precise)
“Avian” or “Avian dinosaur” just means a particular branch of dinosaur that gave rise to modern birds. As opposed to “non-avian dinosaurs”.