An important detail in the intro. The blue beast underneath Shou has horns, and 3 eyes on its back. It's very likely a hakutaku. (See English Wikipedia for
description, Japanese Wikipedia for
images)
Keine almost confirmed.
Oh, there are also oni and kappa in the intro, but we can safely presume them to be generic stand-ins for evil forces. Hakutaku though, is an oddly specific creature of good fortune. It doesn't belong here... unless it means something.
EDIT:
The humans are dancing the "eejanaika" dance, and talismans are raining from the sky, which you should have already known, if you've spent any time looking up the game's backstory.
The scene of humans being massacred by oni is probably inspired by the traditional art genre of jigoku-hen - depictions of hell.
The muscular gray spirit near Futo, I have no idea. My guess is, it's a generic Taoist steward spirit, summoned by hermits to perform various minor tasks that require mythical strength, such as tying up a defeated youkai, or carrying a relic that weighs 100 ton, typically a 黄巾力士 "yellow-turbaned musclemen" in classical Chinese novels.
...With that said, its pose look familiar. It's some Buddhist thing I've seen.
Ideas others have contributed:
The "evil dragon" Shou is fighting is "Itsumade" a.k.a. "Till When", a.k.a. the strange bird that Hiroari shot (see the image
here for comparison). The story of Hiroari is modeled after the shooting of Nue, and the bow in both stories are the same one, but strictly-speaking, Itsumade is not Nue.
The river at the beginning is Sanzu River. It's written on the milestone beside it, and there's a soul floating above it. The mountain is Youkai Mountain, notice how the "clouds" have faces, beaks and a fan - they are tengu.
The lone monk with a hat might be Yuyuko's father. The nun walking with a stick might be a reference to Byakuren's past life. The child underneath Shou might be Akyuu.
You can see what might be a dragon's tail near Reimu. "Like a dragon, you can only see either its head or its tail."