Um, this is basically an animated version of a thumbnail grid, right? I think I would try out a CSS based approach first. CSS3DRenderer can be useful in this context. The following example might be a good starting point:
In general, you don’t need necessarily an engine for such an app. This can also be implemented with plain HTML, CSS3 and JavaScript. You will find a lot of example for responsive grids and content carousel in the web e.g.: