Photomatix defaults and algorithms do not change, although stuff is added. I can still open .hdr files from v3 and get the same results.

Here's your answer, obtained in five seconds by googling "Photomatix Nikon D 810". From their FAQ:

While the current versions of Photomatix Pro and Essentials do support RAW files from the Nikon D5300 and D810, it only works with 14-bit NEF files, not with 12-bit ones.
We will fix this issue in a future version, but in the meantime you can avoid it by setting your NEF Preference to 14-bit instead. Another option is to convert your 12-bit NEF files to TIFF or JPEG in a software that support them, and then load the converted files in Photomatix. This workflow has other advantages, as further detailed here.

Photomatix defaults and algorithms do not change, although stuff is added. I can still open .hdr files from v3 and get the same results.

Here's your answer, obtained in five seconds by googling "Photomatix Nikon D 810". From their FAQ:

While the current versions of Photomatix Pro and Essentials do support RAW files from the Nikon D5300 and D810, it only works with 14-bit NEF files, not with 12-bit ones.
We will fix this issue in a future version, but in the meantime you can avoid it by setting your NEF Preference to 14-bit instead. Another option is to convert your 12-bit NEF files to TIFF or JPEG in a software that support them, and then load the converted files in Photomatix. This workflow has other advantages, as further detailed here.

It's a codec. You can get it here:

http://downloadcenter.nikonimglib.com/en/products/170/NEF_Codec.html

But you already found it and it is working, so this is for anyone else looking at this thread.

To the OP, what are the specs for your computer. I use a D800 and routinely process 5 shot HDR, but also do 30 shot focus stacks, and the largest pano I've merged is 18 frames, for an image that is 41,000x7300 px which results in a 300mp image. My computer is slow as expected, but it doesn't crash.