Another way to say this is that what is commonly referred to as the American dream is in direct contradiction to the law of rent.
The article chooses to phrase "the American dream" as "The American Dream begins with a good job and place to live that you can afford." Generally in this context 'a good job' is taken to mean that the pay and benefits offered as compensation elevate you comfortably above the total cost of living. As you pointed out, if a lot of people are colocated in a region with a scarcity of minimally-acceptable housing, then the first condition of the American dream (that a lot of these people have compensation comfortably in excess of the cost to live (e.g. the cost to buy the property they want)) necessarily implies that prices will be bid upward just to the point where all of the "comfortable excess" that the compensation-above-cost-of-living is eaten up by the elevated home prices.
So the second condition of the American dream, ("a place to live that you can afford") can only be fulfilled if you change your perception about what kind of home you want -- and so a lot of the article can be understood as describing a preference shift in Millennials (and many others, for example I am a bit older than Millenials but also face this dilemma).
Instead of preferring "normal American family homes" as have been readily available in many good-to-live-in places for about the last half century, we now have to say that that preference is no longer an affordable preference to have (even though probably most of us are unhappy that changing world circumstances has dictated this change in the affordability of the preference, and feel it is an overall bad sign for world economic progress). And we replace the preference with what seems to be more of a desire for social mobility, urban amenities, and proximity to very large employment hubs.
The inevitable tension between the two components of the American dream, good job and affordable house, has caught up to us, which is perfectly predictable, and in response, it seems social mobility is more preferred than preserving the sort of American 'family home' lifestyle by foregoing wages and social mobility in order to live in a more affordable area.
I expect that a lot of this has to do with status signaling and money, and probably also mate selection. The relative gains in status to pure wealth optimization seem much stronger now than before -- even if wealth was still the most dominant part of status in the past. This is anecdotal, so I could be very wrong, but it just seems to me that you could earn a lot less, but establish a family home, and still be a high-status member of a community in the past.
But now, it's just money.
It doesn't matter if you've built your own, stable life in a small town community in America, and you've done so with extremely impressive hard work, frugality, and wits, while also supporting and nurturing a family. If you do all that now, but you don't earn a high wage, you're treated as a total nobody for society to shit on and mock.
But if you spend all day doing things that are arguably bad for society in a cubicle farm in a skyscraper and go home to a tiny apartment in a city where you'll never be able to buy property, yet your salary is in the top 25% in the country, you're treated like you deserve respect and like you are a productive member of society. More or less.