You can't use triangulation for anything over a few light-years, the angles are just too acute. And even then, you need to use the full width of Earth's orbit (i.e. repeat a measurement at different times of the year).

I think they just know what the frequency distribution normally is for a burst like this when it is emitted, and use the redshift of the measured frequencies to estimate the distance. Plus they correlate it with the apparent source based on direction (a certain galaxy, in this case, which helped confirm the distance estimate).