AE's 3D space is often referred to as 2.5D as it is often lacking when trying to do "real" 3D things. My initial thought is that this wasn't done in AE and trying to do it in AE is going to be a whole lot of extra unnecessary work (like trying to use AE as an NLE).
If you are insistent, then it looks like its mostly just write on effects in 3D space. If you are okay with your final being a bit more flat (postcard 3D which is what AE does), then it shouldn't be too difficult. But there are a lot of subtle movements that will be very difficult and time consuming to fake in AE rather than a proper 3D environment.
the way the paths are revealed and the rather simple perspective motion makes me thing this was done in Ae and properly faked to give the impression it was 3D. here's a nice tutorial about how to achieve it: