Intel chips are not good enough to run Direct64, and are considered below minimum requirements even for Project64's default plugins. This explains your graphical problems with Doubutsu no Mori as well as difficulties with Direct3D detection in general.
To put it bluntly, what you have is bottom of the barrel.
Get the latest drivers from Intel and stick to using Jabo's Direct3D6 plugin, because that is pretty much the only plugin that will work [adequately] with Intel chips.
That's true if it's an i815, which is ancient, anyways, but G31/GMA3xxx and later not only supports 32-bpp, but also pixel shader!
That's where the bad Intel reputation comes from, the dreaded i815. (circa 2001)
The i815 (a.k.a. 82815) requires that you drop down to 16-bit color and yes, glitches are common!
--> And if you have an i815, then that means your PC is at least 8 or 7 years old!
Seriously, if your PC is at least within 2 years old, there's a good chance the Intel video is going to be fine with DirectX 8.
Infact, with the Intel GMA3xxx video, there seems to be just minor problems with Zelda: OOT, the outside lantern flames don't appear like they should, only a glow and sometimes none at all, but the flames in levels are fine.