Not really. The gap between AMD and nVidia is (currently) a bit smaller in DX12/Vulkan. But AMD still loses.
if you are talking 480 vs 1060 that is not correct
the 1060 is only superior on the Nvidia sponsored Rise of the Tomb Raider, on the AMD sponsored and more neutral games the 480 tends to be faster.
the Vulkan CPU bound testing is interesting and it needs further development (the current patch/drivers fails to even apply vsync properly!)
AMD made a good job with low CPU overhead and high drawcalls with Mantle (plenty of tests showing) and DX12, their problem with high overhead on DX11 doesn't seem to apply to those, also those Vulkan results don't seem to apply to DX12 games.
but I have to say, seeing all the benchmarks being done with just 6700Ks OC and not a cheaper CPU is disappointing, I remember when Anandtech over 15 years ago would test the new VGAs with 2 or 3 different CPUs of significant performance differences.
I think we need that for cards like the 1060 and lower at least, since most consumers don't run 4.5GHz i7s I would think.... and for DX11 alone the advantage Nvidia can maintain with slower CPUs is significant, Vulkan is unexpected, but as I said, it's to immature it seems.
I think Time Spy is solid at trying to be neutral, but reality will see some Rise of the Tomb Raiders and some Hitmans, favoring each vendor due to deals they made 😐