Airtight isn't really the best way to describe it. Rather it's controlled air exchange, this way instead of 1000 tiny leaks all over you have a central controlled means to exchange air.

Passive home typically have ERVs or HRVs (Energy/Heat Recovery Ventilators) to achieve this, they can control the heat/humidity in the air.

Has to be some kind of air exchanger

Reading through the article suggests that they aren't completely airtight, rather that the air comes in and out through mostly only through specific paths, with some sort of system that exchanges the heat with air leaving the house, so that the heat (or lack of heat if keeping the building cold) does not leak out much when the air circulates through.

Here is a schematic I found on the Swedish version of this article: https://upload.wikimedia.org/wikipedia/commons/0/00/Passive_House_scheme_1_multilingual.svg

I suspect not all passive houses are built in this except way though.

The WSJ article has a diagram explaining the air stuff