Fair point, though the post is written in gender neutral language, perhaps to shield privacy. In that context, “child” is probably the most natural word to use?
I had a similar reaction, but on reflection, I think if I were trying to describe my relationship with adults I am a parent of, I would still have to describe them as children.
I don't think I agree that this is common language.
The simple form of relationship is "our children" or "my parents", clarifying the age bracket isn't normally used. I say this as someone with 2 children, one is 19.
In some contexts I may describe my parents as "my elderly parents", but only if the age context is relevant.