I have watched the video carefuly and I believe this has been done that way:
After designing the main graphic (just the yellow line) it was separated in different objects for each line or group of lines and uncovered with masks. I can see it in some curves where the yellow appears as uncovered by a line, not a vector paint progress. Check out the lowest yellow line in the r of poetry, for example. Separating it into layers allow to change colors and moving words as they do, and blik.
All this got then probably precomposed and the effect of drop shadow was added. By the way, if you want to add several drop shadows as they did, I recomend to start with a distance of one and increase it exponentially after that, starting with 2 in the second effect, 2,4,8,16.
I presume they did something BEFORE that, they put another drop shadow with the same properties but in the opposite direction to end covering the yellow part with a full stroke line. I think
the best way to keep everything in control is with expressions, so you only have to animate the values at the first effect.
Finally, check out a little mistake (or is it?) there: Parts that are not onscreen don’t project shadows, like the line that goes over the “h” of “they” at the end. Just like the drop shadow effect does.