You don't really have a passive air flow system as the air pump at the bottom of the setup is introducing air into the system actively. This system allows for movement of water without the need of a water pump. Water pumps can require a lot of power, especially the higher you need it to pump up.
The air holes in the lid just make it so that the system can have the same temp, humidity, pressure as the outside so it doesn't have to work as hard. Plus if it was really humid you wouldn't be able to see it, and isn't it a masterpiece to be observed

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I'm assuming you meant passing air through closed tubes circulate water. Well when you introduce the gas into the liquid it can create a pressure, that small build up of pressure as well as the speed at which the bubbles are rising cause some water to exit the photo portion of the reactor and go into the reservoir on top. This increase in water pressure pushes water down into the photo portion of the reactor. Same principle as water pressure causing a toilet to flush, just not as sudden.
Hope that helps.