Not sure what you are asking. All I see is a lot of hard cuts and as much as I scrub through the whole 8 minute piece, I can't find anything that would be different or complicated. If there is anything specific, you have to be more precise. Or do you simply mean the subtitles?
Yeah, my bad for not making it clear. I'm talking about the specificalized subtitles. At 1:22 in the video, the upcoming three subtitles each have some sort of fade out effect where it sort of looks like it's being scratched/scrubbed away.
You can use anything in AE as a matte for another layer. That is to say, you could animate a black paint streak/scratch on a white background in a precomp and use that as a track matte for your text.
Alternatively, you might be able to use something as simple as a Linear Wipe with the Roughen Edges effect.