The Wii U did 'compete' on performance in a not dissimilar way to how an xbone level system would compete if it was launched at the end of this year. I don't think saying it's 'unique and different' sounds like it has anything to do with processor power. It could mean it uses cartridges for all we know.
I think an XBO-level machine launching this year is very different to the Wii U in 2012. In 2012 it was very clear that there would be a complete generational shift a year later, and that, with a couple of exceptions, development on PS360 level hardware would dry up very quickly. This time around, if Sony is to succeed with their "mid-gen revision" approach to the PS4K, then support for the PS4 has to be maintained for at least two or three more years. Ditto with MS if they do release a new Xbox.
I'm not all that confident that third party games will be at all optimised for XBO and PS4 going forward (as all screenshots, videos, previews and reviews will be based on PS4K/XB1.5 versions), so it would seem to me that Nintendo would end up with maybe three years of third-party games with sub-30fps frame rates, but that's still a better situation than they were in with Wii U.
Yes, Kimishima could mean they're using carts, he could mean NX is going to use lasers to beam images directly into your retinas. But when he says "we have to move away from those platforms", it's clear that they've had to re-think the approach they've taken with the Wii and Wii U, and part of that approach they're going to have looked at is the decision not to target performance and the effect on (particularly western) third party support that decision had. That's not to say that they're definitely going to re-enter the hardware race, but they've definitely thought about it, and there's no way of knowing what the results of that have been.
The other aspect to keep in mind is that, if Nintendo drop Wii U BC (which seems likely), they've got a very different decision process for the NX hardware than the Wii U (or Wii). For Wii U they necessarily had to absorb and build on the Wii architecture, as it was obviously designed from the start as having BC. With NX they've gone to AMD, and AMD would have said to them "You can have 12CUs for $X, 16CUs for $Y, 20CUs for $Z, etc., etc.". They have to ensure sufficient memory (both quantity and bandwidth), but it's actually very simple this time around for them to maximise performance given a particular silicon budget, as they're working with a pre-existing, inherently scalable architecture.
Effectively, Nintendo will have taken the BoM of their controller, mainboard, case, cooling assembly, hdd/flash memory, etc., they'll have decided what price they want to sell it for (including what loss, if any, they're willing to take at that price), and then they'll have taken whichever SoC and RAM fits within the budget that's left.
If their controller innovation is cheap to implement, and they plan to sell the console for $350-$400, then they shouldn't have any difficulty putting out a console that's noticeably, if not massively, more powerful than PS4. On the other hand, if their controller is expensive and they want to price the console at $250-$300, then obviously it's going to end up a lot less powerful.
The Wii U was basically the worst of all worlds in this regards. They had a very expensive controller, a $299 price for their entry model, and an SoC that was very expensive for its performance level. This time around they're going to have the same options in terms of perf/$ for their SoC as their competitors, and it pretty much just comes down to how expensive their controller is (with something as "unique and different" as the Wiimote, they should be able to match the PS4 even at $300, with something as "unique and different" as the Wii U Gamepad they won't). As we have pretty much no idea what they're going to do with the controller or how they're going to price the NX, it's near impossible at this stage to make
any kind of estimation of how powerful the console will be.