Because the waves are what makes the stars and system burst out causing the galaxy to make its spiral shape and maybe this is the way they read the galaxy, we humans use telescopes etc they might use some sort of gravitation wave scanner of sorts, read the article it isnt only about two merging black holes, its about finding unseen stars and planets
'LISA' and 'PLATO' are unrelated missions - they were just both approved at the same meeting by ESA. PLATO is using stellar dimming to detect exoplanets.
The galactic spiral arms aren't created by gravitational waves, although gravity does have a very important part to play in the motion of those stars around the galactic centre (allowing for weirdnesses such as stars on the outer rim orbiting around the centre faster than those closer in - part of the reason for the invention of Dark Matter). The basic mechanics, however, are effectively the same as they are for planets in a solar system - the initial mass(es) which coalesced into the stellar body acquired velocity from an event which threw it out, whilst the gravity of the mass in the centre of the galaxity keeps pulling back towards the centre - giving rise to an elliptical orbit.
Gravitational waves don't affect that - what they do (in very simplistic terms to the best of my non-science understanding) is affect the distance between two points in space, because they are stretches/compressions in spacetime - how those two objects move
through spacetime, however, is unaffected.