It should. The D810 had support since version 8.6. (A relative newcomer.) Did you use Help > Updates on the menu bar?
Take note that the updates for Camera Raw in CS6 only supports updates for cameras and nothing more. You won't get any of the new features inherent in the versions for Photoshop CC (like the filter brush in the Graduated Filter).
I tried lots of different things but I've since downloaded version 8.7 and it seems to be working now. Thank goodness!!!