The systems that use water still use the typical refrigerant-based cooling, the difference is they use water and evaporative cooling to cool the condenser coils(the hot side, usually cooled with just a fan in typical residential units)

This allows the hot/high pressure side to be cooled to lower temperatures than possible with only air cooling, which increases the efficiency of the unit. Since water is evaporated, this required a continuous supply of new water.

Another use of water is in the distribution of the cooling -- basically using the above system to chill a different water supply, then using this chilled water to pipe the cooling to various areas of the building. This is typically a closed loop system and shouldn't require any additional water over the amount required to initially fill the system, unless there is a leak.