TS; I think you've got it backwards, to me the d810 seems more like a response to the 5D3... the D800 is a great camera, but it was lacking compared to the 5D3 for a lot of shooters in a few ways, all where remedied by the D810, for example;
-5D has more AF modes than the D800 and has been reviewed to track better and clear the buffer faster, now the D810 has similar modes and results
-5D has 6fps, D800 only had 4fps, D810 has 5fps
-5D has better high ISO performance, D810 is now much closer (from what I've read, but in my experience 5Diii definitely has better high ISO performance than the D800)
-5D has higher resolution screen than the D800, D810 now ups the resolution
-Video improvements in D810, it's no secret that Canon has been killing Nikon for video, D810 makes strides to close that gap
To me it seems that Nikon recognized that they were losing the interest of the sports, wildlife and video shooters and the D810 is an attempt (and a solid one) to get that crowd interested in their system again.
In the end though... why does it matter? The 5Diii is an amazing camera, it's no less amazing just because another camera came out from another manufacturer.