Market-rate, as a term, just means that it’s governed by supply and demand and not externally subsidized. The rest of the text describes how loosening zoning laws spurs housing construction which helps with affordability.

The idea is that, if enough housing gets built, the market rate lowers. For instance, my city Montreal has a lower market rate than, say, San Francisco or Vancouver. Why? Higher supply and lower demand.

Or an even better example: Tokyo. Most populous metro area in the world, but it’s also stupidly easy to build apartments and other dense housing by right. The result? The “market rate” for housing in Tokyo is remarkably affordable, even to a minimum wage earner:

Two full-time workers earning Tokyo’s minimum wage can comfortably afford the average rent for a two-bedroom apartment in six of the city’s 23 wards. By contrast, two people working minimum-wage jobs cannot afford the average rent for a two-bedroom apartment in any of the 23 counties in the New York metropolitan area.

…

In Tokyo, by contrast, there is little public or subsidized housing. Instead, the government has focused on making it easy for developers to build. A national zoning law, for example, sharply limits the ability of local governments to impede development. Instead of allowing the people who live in a neighborhood to prevent others from living there, Japan has shifted decision-making to the representatives of the entire population, allowing a better balance between the interests of current residents and of everyone who might live in that place. Small apartment buildings can be built almost anywhere, and larger structures are allowed on a vast majority of urban land. Even in areas designated for offices, homes are permitted. After Tokyo’s office market crashed in the 1990s, developers started building apartments on land they had purchased for office buildings.

https://www.nytimes.com/2023/09/11/opinion/editorials/tokyo-housing.html