tsg-
So far Nintendo is claiming that the NX will be a combination of the two markets in a way. The comments they made around the initial announcement was that they were struggling to keep up development on two separate consoles, handheld and home, at the same time, and that the NX would somehow bridge the gap. They would not and have not gone into greater detail, other than saying they felt it was not a replacement for either device but rather a new type of device (they said the same thing about the DS before it killed the Game Boy Advance or whatever).
There is every possibility that the NX will end up being a portable gaming device (a GamePad with the guts inside of it), or that whatever form of home console it takes, it is merely a stopgap until they put the same guts into a mobile device.
Or it could be a streaming device!
People have been claiming the console/PC market is dying because of mobile gaming, but console/PC games have responded by following the movie industries response to better TV and hardware: separate yourself into huge blockbusters and cheap, unique indies.
The thing coming to take console lunch money in the future, though, isn't going to be hamstrung by the controls, or the screens, or the games. Once streaming services have matured, both technology and pricing, it will do to TV and movies what Netflix has done. You're having nearly the exact same experience you had before, but now instead of sticking a disc into a local box, you're getting it streamed straight to your TV. Latency and bandwidth will become even less of an issue than it is now, and with the predominance of online-connected console and PC games, even "normal" games will require a strong connection.
And if your streaming box has enough power to decode 1080p or even 4K content on the fly, I'd guess it will handle some simple single player games installed right on the box, just to appease people who say it's useless w/o internet (similar to how a Roku can play things off of USB).
So look forward to the future of console gaming, where the console is just a streaming box which can eventually be built into your TV.