Let me see if I get the jist. Am I right in assuming when you waved your phone through the air the motion sensor “deposited” a cross section of text in the air at the right time, leaving in the eye’s persistence of vision or a camera’s slow shutter a ghostly imprint of the whole word? Like those light sticks or LED bicycle spokes?
If you want to do that real time, then AE is not the program for you. Even if you made a movie of the effect I don’t think a phone or tablet would play it fast enough and rip through enough frames to place the effect in the air with enough temporal resolution. Plus you have to time the doling out of frames to the speed of the phone’s motion. It’s hard enough to maintain a steady frame rate on a phone when what’s really needed is a constantly and hyper accurate changing frame rate tied to the motion sensor chip. A custom video player would be needed or an app that generates and displays it on the fly like the app you mention.
But if you want to simply recreate the photos with text imagery over top, yes it can be done in AE but might be easier in a 3D package like C4d (and then into AE for the comp).
The key is the shader used on the text. You want something that has transparency, probably an edge hilighter (like a fresnel), and you may find that text built in 3d might be better constructed as a shell with thickness as opposed to a solid. A shell version will give more character (pun intended) to the letter’s edges.
Then simply composite the result with a screen blend function on to your background image – light in the real world adds up over what’s behind it and “screen” does this beautifully (ironically “add” can build up too much).
In AE zaxwerks or Element 3D could get you there for the 3D text (and there are a few others). You can also do 3D objects in Pshop if still are all your are after.