"Pledge $1 or more (7525 backers) For just $1 the iOS App is yours!"
The iTunes store doesn't actually have a mechanism to achieve this, does it? Other than making it free for everyone for quite a while (months?) and using promo codes to fix up any backers who didn't download it in time. Promo codes are limited to 50 per release, I believe.
There is another way to achieve this (but apparently the developer didn't do this).
Make a second version of the app that requires a login. Give the login information to your supporters. IIRC you can even put an app into the store and set it not to appear in searches(?), then you need also to hand out the iTunes url.
According to the project homepage[1], the Android and iOS apps are "coming soon", and his twitter says he submitted them on 2nd Jan[2].
There is also "Life In Seconds"[3] which has a few good reviews, and a "1 Second Daily Cam" app by Simon Meyborg but that has five one-star reviews on the iPhone UK app store.
A similar idea is One Second Epic[4], which also looks promising.