If you want to measure a gravity wave, you just need a big block of concrete embedded in an underground cavern of jello, fully instrument it, and wait. This block has accelerometers and ring gyros to measure the rotational components, as it shakes in the jello.
Problem is that this nasty earth has all those earthquakes! And you can't easily filter out the effects of seismic waves. And really, you need a whole bunch of blocks in jello to detect a gravity wave. Thus, they developed the sensitive rotational sensors that you need for the task, both for the block, and the rock all around it.
Look at this guy just preparing the glass block for a ring laser! These things are expensive!
Ok, they got the cost down by using fiber loops, and other little tricks. Now they can be dispersed in the field, but what are we looking for?
One reason that a ring laser may be quite good for gravity waves is that we generally can't expect rotational waves in the rock. A real torsion wave is something we propagate down a cylinder by twisting one end rapidly. The pure rotation can only be measured at the centre, and out from there we get a mixture of translation and rotation. Torsion waves are almost impossible to propagate in an elastic half-space (which is the earth).
Nope, our seismic waves are plane waves, which set up a front and propagate rapidly. For the shear wave there will be out-of-plane rotations, and they might be interesting to measure, but the amount of rotation falls directly from the plane wave equations, and translational measurements are most likely enough.
You can get complex rotational waves and effects right near a complex fault, where all the plane waves intersect, and I can imagine a tight rotational wave propagating for a short time. This makes life more deadly near a fault, and would be a good place for these new sensors.
In fact, any complexity will start things 'spinning'. A soil basin could easily hold a rotational wave, imagine a bowl of jello that you suddenly twist. Like a cylinder wave, the maximum vertical axis rotation would be at the centre of the basin. There would be horizontal axis rotation with surface waves.
It is with surface structures, that there is observable rotation. Images just as these have haunted 'rotation fans' for generations.
I don't think much of this, but some people do. Nevertheless, when a building starts to rock, things become much worse. Rotational sensors could sort some of this out.