Yes, spec-wise the Z6 looks like an A7ii w/o eye-AF, the Z7 like a A7rii w/o eye AF. That tells me enough (especially since they now promised eye-AF in their firmware update)
The specs do look similar, but it is hard to come up with a significantly different spec list given the features of the D8x0 series and those of the Nikon 1 series from which Nikon is transitioning. Part of the team that worked on Nikon 1 continued their work on the Z series. Although Nikon 1 was not a commercial success, Nikon experimented with many technologies there (and some of them have yet to be transitioned to the Z series).
For example, Nikon pioneered* the "hybrid AF" which successfully combined contrast-detect with on-sensor PD - it was the first implementation in a MILC. For many years after that, Nikon 1 cameras remained the best in MILCs at tracking (erratic) action. I am sure that Nikon will further improve the AF capabilities of the Z series to bring them up to speed with the competition, and will do that sooner than many expect.
As for Eye-AF, I don't believe that Nikon is willingly copying Sony - its the people that screamed for this feature on the internet and through other channels that made Nikon do it.
When it comes to timing, I agree that Sony influenced that a lot. I believe that Nikon would have released a FF (or an APS-C) mirrorless camera in a couple more years anyway, but Sony forced them to move faster. The first Z cameras do seem a bit rushed.
Nikon has been in a cost cutting and production simplification mode for many years now. When they released the first Nikon 1 cameras they talked about the reduction in the number of required parts that they were able to do compared to their other DSLRs at the time, as well as the reduction in manufacturing/assembly costs. It was only a matter of time until they would have switched their other lines to mirrorless for this reason alone.
But, without Sony, they would have probably started with the APS-C line and then FF, and possibly with the consumer cameras first, then enthusiast, and finally their pro cameras.... Would have, could have, should have.... who knows.
In any case, just to repeat what I said when the Zs were announced - I am not onboard for the cameras, but for the new mount and its promise of better optics. So far I don't consider that promise to have been fulfilled, even though the first 3 lenses have some very good reviews. I expect the best is yet to come, after the optical engineers get some time to test the boundaries of the new mount. I am looking forward to see how the announced 24-70mm f/2.8 S measures up.
* I know that Fujifilm was the first to release cameras with hybrid AF in July 2010. But their implementation wasn't so good, it was in P&S cameras with fixed lens, and by that time Nikon was already working on their solution which they released one year later with the V1 and J1.