As with many such things, this looks really cool in a video and I cannot think of a single possible practical or even fun use for it (super gimmicky game?), and a bunch of reasons it would go right past useless and into actively making things worse.
Without significant software modification it would be an active nuisance in just about any app--imagine the UI mess if the app thought it could actually use that space without knowing it was on the edges. Forget that it instantly becomes a normal phone with a case on--if there somehow was a thing that actually used it, now it's actively hidden from view.
My favorite part, though, is that it precludes using a case, and then adds a screen on exactly the parts you're most likely to drop the phone on, so it not only increases fragility but makes sure you can't do anything about it.
I'm sure there are use cases for a multi-direction curved screen, this just isn't one of them. At all. If they were going to make a gadget to show off the tech, why use a phone instead of something that doesn't go aggressively against how the device is supposed to be used.