I can't see how immigration can be considered to have no impact on available housing. People have to live somewhere and if there were fewer immigrants, there would be more housing stock for non-immigrants — unless you believe that immigration causes houses.
It's perfectly possible for immigration to be a net positive for the economy and for it to have negative affects on the availability of housing.
There are approximately 14,072,080 occupied private dwellings in Canada. The rental of 31,000 of them on AirBNB is unlikely to be a significant factor in the housing shortage.
As the article states, 31,000 is 1.5 percent of rental accommodation. If we assume that half of the 300,000 immigrants rent, and that they tend to rent in couples, that's 75,000 rental properties consumed by immigration each year -- or about 3.5 percent. That's an additional 3.5 percent of rental housing stock each year, a much faster increase than the number of AirBNB rentals.
Regardless of whether you think immigration or AirBNB are major causes of a housing shortage, it's disingenuous to argue that immigration has less of an impact than AirBNB.
EDIT: It's also worth noting that construction is expected to slow over the next five years, whereas immigration is expected to grow.
It's perfectly possible for immigration to be a net positive for the economy and for it to have negative affects on the availability of housing.