It looks like you are using an ad blocker. That's okay. Who doesn't? But without advertising revenue, we can't keep making this site awesome. Click the link below for instructions on disabling adblock.
Yea, id say after effects. you can do anything in there.
Go here http://www.videocopilot.net/tutorials/ if you havent before and follow some of those to get a feel for what everything does and then you should be able to venture out on your own and try some things like in the Slamina clip
Import all the files you want as the small thumbnails in AE, make a new comp and put them all in the comp, just order them however you like.
Make a new camera layer and a null-object. Parent the camera to the null-object.
Then, make everything 3D (make the layers 3D). Animate the camera, by keyframing the position and make it follow the path you want it to go.
Lastly, keyframe the opacity for all the 'thumb-nail' parts so they appear whenever the camera comes by. Of course it won't look nearly as good because there's no 'extra' stuff to make it look cool, but I'd say that's the basic concept (I hope, hehe)
I'm not claiming to be an expert here, but I think that would make it look 'almost' the same!