That is a simulation of a projector that has the shutter out of sync with the pull down so you see the frames moving. You would simulate that by fussing with the frame rates and using frame blending or motion blur and possibly some fooling around with blend modes.
The first thing I would do is download the clip from YouTube and start counting frames. The best way to duplicate an effect is to look carefully at the frames. I am guessing that the sequence is running at about eight or ten frames per second so that it takes about 3 frames for each new frame to move into place and then it sits there for a frame. This is a guess from this random still from the sample video. It looks like about 1/3 of the frame is covered by motion blur. Let's say you choose three frames of movement and one sharp frame. You would create a comp with a bunch of images. Choose all of the layers and set the CTI to 7 frames and set the out point of all the layers. Seven frames so you can have 3 that move, one that stays still and then 3 more with no movement to give you time to reveal the next image.
Now you set a keyframe for position on frame 3 in the default position. Now move to frame 0 and move the first image up and out of the frame by about 1/3 to 1/2 of the frame height. Move to frame 2, turn on motion blur and start jacking up the blur amount in the Composition settings by adjusting the shutter angle and shutter phase so that you get a frame that pretty much looks like the first frame in the sample clip where a new image is moving into frame. Make it look something like this:
Check the second frame and the third.
If everything is ok save an animation preset for position. Select all other layers and apply the animation preset so they all move into position and stop in 3 frames. Now select all layers and sequence the layers using the Keyframe Assistant setting the overlap to 4 frames. You'll be able to figure out the exact overlap if you have counted the frames in the sample video. If you have set things up so the look of the first overlapping frames gives you something like the thing you want you should be done.
Then it's just a matter of pre-composing this sequence and setting up a track matte to reveal the title.
My impression of this sequence is that they are simulating flip book-style animation. Could even be a vertical zoetrope but that's a stretch. You could do this manually. Research the technique, collect interesting images, copy them to the same and suitable paper stock, staple them together, flip them off your your thumb. You can shoot it with different cameras and shutter speeds to simulate the blur in camera or apply it in post.
Thinner or larger paper stock will curve more than stiffer stocks. With a large aperture and very selective focus you can create your own take on this.
Thanks guys you are both legends.