Difference between the case posted there and the chiller is that is specific to AC, and air has terrible thermal capacity.
Looking at peak numbers is misleading unless the laser is running non-stop, and doesn’t account for a holding tank.
The current set up just pumps water through the laser tube into the cooler, that the AC in turn keeps at a lower than ambient temp?
Any volume of water is going to have a huge amount of heat capacity. You need to dump 4100 Joules(W-s) into 1 kg of water to raise it by 1deg Celsius. The existing cooler is about 27L or 27kg when full, so it takes 111,000 Joules to raise that 1 degree. 120 seconds of continuous cutting.
I don’t know the efficiency of the chiller, say the 180W runs @ 50% efficiency that would take roughly 10x the amount of time as the laser cutter runs to bring it back down to temperature.
Factoring in time for movements without cuts, time to change stock, programming etc I doubt that the cutter is actually working for much more than 1/10 the time it’s being used.