I wouldn’t even call it a text animation. To me it looks like it’s just popping up a white box over each text area and then changing the transparency to reveal the text behind it. If I were doing it I’d create a text layer for each word (or group of words) you want to appear, then create a white solid for each one of those. You could scale or mask the solid to completely cover the words. Then animation would be as simple as lining up the corresponding text layers and white solid layers and putting a 6-7 frame “dissolve out” on the white solid.
Even if you were really slow, I’d say it shouldn’t take but a couple hours to do.