You are taking into account the entire population of the country while calculating the displacement of the population, while Airbnb units this article is referencing tend to be concentrated in certain neighbourhoods of certain cities. Your calculation is off by a mile.

Airbnb’s tend to be near central business districts or other attractions.

If by offering short term rentals you take 30% of the rentals off the market (which may only be 100 apartments), that has a huge impact. Rental prices are all about marginal demand.

There are other factors as well — there is a de facto price floor due to section 8 prevailing rent. Because of factors like the “just build” doesn’t work, as profitable new construction is high-end, and the older stock tends to turn into defacto hotels.