I like the design, and it's a neat idea, but I have a couple of concerns:
1. Those edges look sharp. I hope they have thought of this and made sure to smooth out any edges where your hands naturally rest. As long as they do that, the edges everywhere else can be sharp and it won't affect anything.
2. That screen is a nice idea but one thing comes to mind and that is cost. These things might up being as expensive as the Wii U gamepad and you need at least a couple of them if you want to enjoy multiplayer games. The second screen thing has been around for a long time already, with the DS/3DS and then the Wii U, and while for the most part it wasn't used for anything special, having a small secondary screen to show HUD elements, map etc to keep it off the main screen isn't a bad idea, at least when done on a handheld. On the Wii U I found it was a hassle to keep looking down at the gamepad for games that required that, and having to take your eyes away from the main action can be a bad idea sometimes. But there are cases where having a secondary screen is a big deal, for example in Four Swords Adventures and how that game used the GBA screens, I thought that was a really cool concept. Games like that wouldn't be the same with everyone on one screen.
I don't really have any objections to putting a screen on the controllers, as long as the price isn't crazy, and it's actually used for things that justify having it there. I'm not too concerned about battery life, because the screen's not that big, and OLED (which I assume is what they're using here) is very power efficient when displaying a mostly black image.
The usage cases in the concept images are a good example of the entirely wrong use for an in-controller display. That's just gonna make you have to look away from the main action to check basic information, and that fraction of a second can mean the difference between life and death. If that's the best they can come up with then they clearly haven't thought this through.
Granted it's not particularly important information, so you would very rarely have to look down on the controller in those specific examples. I'm just worried that devs will treat it the same way they treated the bottom screen on the DS/3DS and put maps, inventory management, menus etc. on that screen so that you're forced to use it frequently. In singleplayer you can at least pause the game to check the secondary screen but in multiplayer that's often not an option.