The video introduces the body parts in an extremely clear way! While showing pictures, it says:
"You can see that the mother has an opening between her legs. It is called a vagina. Right above the opening she also has a clitoris. The father has a penis and testicles."
"...into a hollow space inside the mother called the uterus or womb"
It doesn't assume any prior knowledge of those names! It is done for a purpose... if a child wanted to discuss body parts (such as their own) then it would be helpful to know the names. Though saying the baby grows in the mother's "tummy" is easier to learn, I think it is good to mention the proper name just in case the child can remember it.
So the video/picture book can show things visually unlike a parent usually does. And rather than saying this thing goes there it ends up naming the items along the way (e.g. the sperm goes into the womb/uterus).
Now by maybe 12 or 13 the child is ready for a more detailed explanation like that video.
Some girls are having periods at the age of 9 (and
giving birth) - something that video doesn't cover at all. I think you over estimate how thorough that video is. It doesn't show an accurate cutaway view of the uterus either - something that is sometimes covered in school sex ed.