The article gets some things right but I don't think it uses the term shortage correctly. I will explain that after excerpts from the article.
Excerpts with my notes in red:
"The pandemic has aggravated the housing market’s longstanding lack of supply, creating a historic shortage of homes for sale.
Buyers are accelerating purchase plans or considering homeownership for the first time (demand increases), rushing to get more living space as many Americans anticipate working from home for a while. Many potential sellers, meanwhile, are keeping their homes off the market for pandemic-related reasons (supply increases).
The combined effect has created an extreme drought of previously owned homes for sale. At the end of July, there were 1.3 million single-family existing homes for sale, the lowest count for any July in data going back to 1982, according to the National Association of Realtors. In the week ended Sept. 12, total for-sale inventory was down 29.4% from a year earlier at the lowest level since at least late 2017, Zillow Group Inc. said."
"The shortage has pushed home prices higher (no, the increase in demand and decrease in supply pushed prices higher), stretching the budgets of many middle-class and first-time home buyers. The median existing-home price crossed above $300,000 for the first time ever in July, up 8.5% from a year earlier, according to NAR. Existing home sales and inventory figures for August come out on Tuesday."
Given that the article says that "total for-sale inventory was down 29.4% from a year
earlier," quantity has fallen (which is not a shortage, see more below) and that demand increased at the same time supply decreased, then supply must have decreased more than demand increased. This is shown in the following graph.
The intersection of D2 & S2 is clearly to the left of the intersection of D1 & S1. So equilibrium quantity has fallen, just as the article says. And prices have gone up. The article says " The median existing-home
price crossed above $300,000 for the first time ever in July, up 8.5%
from a year earlier." But again, there is not shortage because we are at the intersection of supply and demand. Quantity supplied equals quantity demanded. That is equilibrium.
A shortage means that price is below equilibrium and quantity supplied is less than quantity demanded. This is shown in the next graph.
Now maybe there was a shortage temporarily. Suppose the green line in the graph below tells us how much the price was before supply and demand shifted (this is the same as the earlier graph). The two circled points show that quantity supplied could have been less than quantity demanded right when the changes hit. But sellers would have quickly realized that demand must have gone up given so many people coming to look at their houses. Then they could raise their price. Maybe there was a shortage but it did not last long.