How does open fermentation yield alcoholic beer?

Ethanol boils at 78.4C water boils at 100C, impurities in solution increase further the boiling point of these solutions. Unless you are heating the solution to >50C the rate of evaporation will be negligible. The strong surface tension of water also limits the evaporation from solutions.

Also, you have to think of the surface area to volume ratio of an open fermentation, mostly there will be a relatively low SA/vol ratio, unlike a puddle which will evaporate quickly as the SA is high in relation to the volume.

Think of how quickly the water in your bath at home would evaporate with only a few inches of water in, unless you were in a heat wave it would likely take a good few days/weeks for it to evaporate away.

Even in a Belgium style cool ship they are generally 18-24in /45-60 cm deep, and kept at a low temperature <20C. The original idea was to allow hot wort to cool quickly in the shallow vessel and they stop the metabolism of the yeast increasing the temperature of the wort/beer too much by allowing convection and low amounts of evaporation to carry away the heat.

Another thing with open fermenters is that they lower the pressure on the liquid compared to a closed fermenter, this helps to reduce the stress on the yeast and leads to different flavour profiles from the same combination of yeast and wort.

Alcohol doesn't evaporate that quickly. We might as well ask how the water stays in the beer too.