The interesting part of this test was that it was a non-line-of-sight contact, which in some ways is more challenging than laser EME.
Laser EME signals travel further, but they get some help. First, the power density of the laser is probably orders of magnitude higher than the 60-LED array used by the Australians. Second, the last time I checked the laser distance measurement used a retroreflector array placed on the moon by one of the Apollo missions, but this may have changed since I last read about it. Using mirrors to direct the beam back the way it came, with roughly the same divergence as it had coming in, is much easier than relying on diffuse scatter from the moon's surface. The last "benefit" is that much of the path traveled by the laser beam is through free space, which does not absorb light. True, the light has to pass through the atmosphere twice on its round trip, but the density of the atmosphere declines roughly exponentially with altitude; the 288km low-altitude path across the Bass Strait may actually absorb a larger fraction of the beam than the EME "vertical" path, but I'm not sure of this.
But as I said above, this is a NLOS pass, i.e. this optical signal is propagating through forward scattering and refraction, like we see with HF signals. The challenge is that the scattering particles are also strong absorbers, so the weather conditions have to be just right to allow for enough bending of the light beam while letting enough get through to detect on the other side. I believe there was a German op who liked to do 10GHZ in the rain, using raindrops to scatter is signal beyond line of sight, and this is the analogous process in the optical regime.
A nice experiment, I'm impressed.