Great find! This is on my want list. I mentioned it in my persimmon article too.
We call it astringent, because of the pucker factor before it's ready. Not all persimmons are like that though, only the astringent varieties. Other non-astringent ones, especially among the Asian cultivars (like the fuyu) can be eaten while still crisp, like an apple.
I've not tasted this yet. But I do have a place in my yard that really needs a tree!!