With Nintendo getting into mobile gaming and the success they're enjoying with Miitomo and Pokemon Go, I expect the NX to have some integration with those games, and mobile gaming in general. Kind of like what Wii U tried to do with TiiVii, but tying in features from your mobile games and apps. I can't get into mobile gaming at all, so I won't use it except perhaps what's necessary to get the most out of my favorite games, but I can see how that would be something they would explore with a new piece of hardware.
As for a core focus, unless what I mentioned above (or whatever Nintendo's angle for the new console will be) lights a fire under people like the motion controls of the Wii did, I can't see the system getting any more attention from 3rd-parties than the Wii U did.
Even when the Wii took off and everyone and their grandma bought one, 3rd-parties kept most of their main franchises away from the system because of a perception of the buying habits of Nintendo's customer base. That perception won't change just because of a neat mobile-integration system or the like. They'll give the system one-off experimental new IPs and then hang it up when they don't sell as many copies as a real effort might. The cycle will continue.