There are a few different ways one could make this look, but here's one recipe. Create your text and using hold keyframes, animate the scale and position very quickly. Use 3 or 4 keyframes, so it jumps from frame to frame, changing the position and scale...use your own judgement.
Add an adjustment layer and add the effect Distort > Turbulent Displacement. Change the displacement to horizontal and adjust the amount, size and complexity, keyframe the evolution. Now just add some masks to the adjusment layer, so the effect is only on a portion of your text. Also in the video it looks like he added some subtraction masks to the text itself to make some of it disappear.
I made a quick little project showing you what I did, hope it helps.
"I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work."
---THOMAS EDISON on inventing the light bulb.