How I can make exactly that text effect in AE? (video example)

I don't see anything but some extreme motion blur on a text box that is scaled up in the X axis. 

An HD comp, Shuter Angle to 360, A blue text layer, an off white rectangle, Anchor point set right over the "I" on both layers because that how I wanted the text layer to grow scale animated from 0, 100 to 100, 100 over 10 frames. Here's what it looks like halfway through the animation.

If that isn't what you are looking for we need a lot more detail in your question.