These rooms have ventilation (and also usually a heater, cooling, dry mode). The ventilation can be set to 24/7 mode, which runs at a low setting, always on. Japanese houses/apartments also typically have a house ventilation system, meant to run when it's humid. Mold in general is a problem here, so ventilation is incorporated well.

It's fun in the winter when you're running humidifiers but forget to turn off your house ventilation and don't understand why you're still so dry.

Not a resident but I have friends there and stayed in a bunch of different apartments.

Bath rooms in smaller apartments, and also in hotels, tend to be, literally, whole-room plastic/resin structures, so it dries easier and if mold appears it's in the plastic surface and easy to get rid of it.

I have a friend with a very big fancy apartment, and his huge bath room is covered mostly in tile and has very good ventilation. The bath even has a waterproof TV so you can watch a movie meanwhile!

It's 98% humidity for months, you need to worry about the whole house!

Unfortunately, it does build up from time to time, yes. However, there is another feature to most bathroom units, which is the room drying feature. It sends warm dry air into the bathroom to dry it. It is also a great tool for the 6 months of the year in which drying clothes outside is impossible. Even so, the appearance of mold can feel inevitable!