From what I've found, they'd be less prone to injury.
Bird bones are hollow and therefore lighter than solid bones of the same size, which is a boon to flying. However, they're also extremely dense. This does add weight - quite a lot, it fact - but it makes the bones incredibly strong, stronger than the bones of most similarly-sized creatures. It also means that the bones are really stiff, which is another good thing.
The fact that they're short shouldn't matter too much, because, as it turns out, bones of smaller creatures aren't any weaker than those of larger creatures. This study determined that
No significant difference (P > 0-2) was found in the failure
stress of bone over a range in size from 0-05-700 kg (233 + 53 MN/m1 for
small animals compared to 200 ± 28 MN/m2 for large animals).
That's a huge size range! So these people are going to have skeletons just as strong as normal humans - if not stronger. You could argue that stiffness could lead to bones being more brittle, but I think the increased bone density could help with that.
The cultural aspect is a bit tougher. You could argue that the strength increase would increase and warlike or violent tendencies in the species, though that might be a weak argument. I don't think it would give the beings any advantages, though, because the decreased height would mean that they would weigh less that normal humans, assuming an equal body density.
I suppose it depends on just what caused them to have to bone density they have. Could their ancestors have be avian? Are they avian? In that case, we enter the realm of bird culture. In early bird-like civilizations, the sky might be revered, and the sky god(s) could hold more sway in mythology than the sun god(s). The ground might be feared, or associated with the afterlife, as the ancient Greeks and Romans associated the underground with death and the afterlife.
"Bone Strength in Small Mammals and Bipedal Birds: Do Safety Factors Change with Body Size?" by Andrew A. Biewener