Edit: I was unable to view the text example you linked.
One way you can do this is to use a clipping mask:
Here is a video which shows how to apply a gradient to text using a clipping mask:
Above video is for PSE 6 but the method is the same. She might call it a clipping group instead of clipping group. (Clipping group = clipping mask; Adobe changed the name not the function.)
Note: Hold in the shift key as you pull the gradient to constrain the gradient so it pulls evenly.