Looks like lots of precomps with lights and shadows. I’ve done similar things in AE and it’s very much possible to do there. I don’t know why a 3D package was suggested for simple animation consisting of flat planes, but you can do this in AE for sure. Getting the look from slide A to slide B will help you figure out what sections to “cut out” and transition. Once you’ve got your slides set up where you want them, I’d precomp them before “cutting” anything (good procedural habit). Use the mask tool to slice up the precomps. Obviously, you’ll need to duplicate the precomp as many times as you need slices. With AE CC the snapping tool comes in very handy to move the anchor point (Pan Behind tool) where you want each slice to pivot. Then go about rotating the slices to reveal the slide below it. I wouldn’t focus on the motion being very technical as I would the style of how you think it should move. The example you gave shows very quick movements, like 5-7 frames (at 30fps) max for each slice. Some of it feels like a transformers transition, which is one way to do it, or at least, one style to think about maybe.
Hope that helps.
Jason Jantzen
vimeo.com/jasonj