Let's look at what we have here:
Firstly is this rumor everyone is pressing on about having a 6" screen in the controller. Clearly this is not going to be an HD screen as some suggest. Even on a phone/tablet that would be a rather tall order and really expensive. Beyond that how do you render to it? Wii only does 480p and 360 and PS3 often struggle to maintain a baseline 720p. To say this console can remote render for this supposed screen and itself is a bit much.
Much more likely here is a reasonable res screen. 320x240 or something. Even then rendering remotely would likely require more than a standard bluetooth connection provides. Unless these are custom controllers, or wi-fi enabled my guess is the controller itself would need to render it's own images. Even if it was remote they'd still need some sort of CPU to decode the images sent and some RAM to act as a buffer. My guess would be an ARM 7 or something. Hardware like this in the controller is going to get pricey. I really don't think Nintendo is creating a new handheld to act as a controller but whatever this thing is it sounds like it'll be positioned as a personal item rather than selected from a communal pool of controllers.
The size of the screen is also questionable. 6" is basically the world's largest cell-phone or a really small tablet. Most point out a Kindle as falling in this range. Clearly this is a bit large for any sort of controller we know of and a tablet is certainly not a good fit for two handed operation (unless they want you on a coffee table). It's also BC with Wii and has new enhanced motion controls. These are clearly contradictory with a screen. The only way to consider both would be if Nintendo specifically branched the controls (which in many ways they already have as have Sony and MS). One branch is a take on traditional controls with a screen and the other is an enhanced wand-based system and the console provides both.
Something here is definitely not adding up with these rumors. My interpretation says this will have some sort of CC with a small touchscreen, accelerometers, gyros in addition to some enhancements to the now standard Wiimote design (likely cameras and magnetometers).