Well, half-toning uses dots (or sometimes lines) to represent different shades. Black the dots are merge into each other, to white were the dots are zero size 
Your white text - no dots, prosably on a transparent layer - no dots The thing is you are fading from white large dots to nothing so probably the example has been colour inverted sometime.
Using Gimp 3.0 (beware those layer effects (fx) You can turn them off on each dialogue - look for the little merge filter tick box)
Starting with the preliminaries completed.
(1) Made the text to suit and from that Layer -> Text to Path
(2) A new layer filled with black, White text Edit -> Fill Path
(3) A gaussian blur applied - value depends on your text / size this one 4.5
(4) Filters -> Distorts -> Newsprint (not a wonderful filter but such is life) Use white on black for the fade out.
(5) Put that over your background. Switch the layer mode to Lighten. Turn the text layer visibility off.
Your white text - no dots, prosably on a transparent layer - no dots The thing is you are fading from white large dots to nothing so probably the example has been colour inverted sometime.
Using Gimp 3.0 (beware those layer effects (fx) You can turn them off on each dialogue - look for the little merge filter tick box)
Starting with the preliminaries completed.
(1) Made the text to suit and from that Layer -> Text to Path
(2) A new layer filled with black, White text Edit -> Fill Path
(3) A gaussian blur applied - value depends on your text / size this one 4.5
(4) Filters -> Distorts -> Newsprint (not a wonderful filter but such is life) Use white on black for the fade out.
(5) Put that over your background. Switch the layer mode to Lighten. Turn the text layer visibility off.