Hi, I like Grahams explanation, but with it also including transparency on the layer prior to it changing I think from what I can see, I would suggest this is how it was done, and a bit more simple way.
1) Create the text your want the end result to look like with words coloured as needed. The demo also shows a drop shadow, so add that as well if needed.
2) Duplicate the text layer (you could also link up the source text to the original, so if you wanted to change the text later on it will update on the duplicate). With the duplicate, place that below the original, and remove the Drop shadow (this is based off the YT sample shown) And add a fill effect to the text layer and pick white/light grey, and reduce the transparency to what you want.
3) Back to the original text layer, Hit Animate (>) right of text, and select Fill Colour> Opacity.
Now open the new Animator 1 > Range Selector. Open up Advanced, an change Units to Index, Change Based on to Words, and turn Mode to Subtract.
Now all you need to do is animate the Start from 0 to whatever number word you want.
I think that is everything. You could also parent the Duplicate to the original and lock the layer so you never have to interact with it, other than maybe adding in an fade in at the start.