This discovery didn't actually involve LIGO, nor any other feats of impressive physical engineering. It was made by observing neutron stars and finding patterns in their unexpected perturbations.

Neutron star rotation is so consistent that they are used to calibrate atomic clocks[0]. However some of them were glitching and not rotating as expected, but the glitches were consistent between each other. It turns out they aren't actually glitching, but spacetime is being distorted by massive gravitational waves.

[0] https://gizmodo.com/scientists-use-spinning-neutron-stars-to...