I have observed that most dry cleaners don't use water or even soap in their operations. They use some chemicals and air blasting equipment which does not look expensive. I suppose in large families and institutions, these can serve as cheaper alternatives to water since time of labour investment when cleaning is minimal. I believe there are other alternatives to water especially in areas with water scarcity.
I remember buying a spray for our divan with cloth upholstery. The spray emits a white foam that covers the dirty part of the surface. As per the label of the can, it is dry cleaning method that doesn't need anything except a dry cloth that you use to wipe off the foam. But the foam is also wet but not very wet as to dry with a dryer. But surely that white foam has chemical for the ingredient because the odor smells like chemical. When we were in the rented house that was a favorite of the floods, we have a neighbor who uses compressed air for cleaning the yard after the flooding. The floodwater is dirty and when it subsides, there is mud and other dirt left. That neighbor has a compressor so his hose is spraying a mist that drives away the dirt and mud. In terms of water consumption, I can say that he had saved maybe 90% of water that we use for cleaning our concrete yard with an ordinary hose.
There may be alternatives but I doubt that they would be cheaper than water. Water is naturally available, however, I believe that there are usually some technical processes in obtaining these alternatives which would definitely make them more expensive than pure water.