Simple cloud chamber construction is described in various places and all seem to use 90% - 99% isopropyl alcohol as a start. What property does this have that makes it an essential component for these devices?
There is no particular property of alcohols; Wilson’s original cloud chamber used water and worked fine.
The essential point of a cloud chamber is to create a supersaturated vapor. Vapors in air have a dew point at which they will condense onto dust and nearby surfaces (like dew condensing onto grass) and they are supersaturated when the dew point is above the temperature of the gas. These supersaturated vapors are then able to spontaneously condense around the wreckage of high-energy particles. Wilson created this high dew point with water by suddenly lowering pressure in a container filled with water vapor; homebrew setups typically use a warm surface evaporating the alcohol into a clear container that is cooled by dry ice, which drops the air temperature below the dew point of the alcohol—although thermoelectric coolers and perhaps even ice water might be able to generate similar temperatures.
Probably the relevant physical fact about isopropyl alcohol is that its freezing point is beneath the freezing point of dry ice, so a layer of liquid alcohol might build up on the cold surface, but it does not start to crystallize at those temperatures. If the liquid crystallizes then it is possible that there is a steady current of vapor out of the air which does not allow it to remain supersaturated, while maybe if the layer deposited remains a liquid, it builds up an equilibrium with the supersaturated air and once this happens the air can remain supersaturated without losing more vapor to the surface.
Possibly the lower boiling point of alcohol also helps (just as certainly the high purity of 99% helps) in evaporating more of it from the warm side of the homebrew cloud chamber into the air inside, raising the dew point therein and making for a somewhat larger cloud inside. But it is possible that in typical homebrew setups this effect is negligible.
On the practical side, I once build a DIY could chamber (using dry ice), and it was working as well with isopropyl alcohol than commercial methylated spirit.
The physical reason is that the physical properties of both alcohol are not so different, as boiling point are just few degree away.