The Galaxy Nexus had a slight curve to the glass (though the display itself was of the standard flat variety). Though some dismissed it right away, I can say I noticed a difference when actually using the phone as a phone — that is, it felt a bit more natural while holding it up to your head. I would guess that any sort of design decisions based around flexible display technologies would have some sort of functional basis. For example, I can see it being easier to reach the top-left corner (when holding a device in one's right hand) with a slightly curved device.
The technology itself isn't a gimmick, but you're certainly right in that we have yet to see any indication of which — if any — manufacturers will 'push the envelope', so to speak, with flexible display implementations.
Edit:
I should add that after watching the videos on the Galaxy Round and its software features (tilt to wake the display up, for example), I would say that Samsung's implementation isn't revolutionary, but it is certainly proper. By that, I mean that Samsung has implemented software features that offer simple but potentially beneficial features to the user, and these features are a direct result of incorporating the new hardware technology. Tilting the phone to show the time, notifications, and battery status is very similar to Moto's Active Display and LG's Knock-On features. My personal opinion of the "Galaxy Round" isn't too favorable, but at the same time I can't fault them for doing anything "wrong" with what is likely the first commercially-available flexible-display phone.
Also, it'll be a while before we see these commercially available in the U.S. at prices comparable to current flagship devices. Notice that the Galaxy Round is priced at 1.09 million Won, which is roughly $1,015.