I don't think there is much argument that cities are generally getting higher buildings.
But, the generalizations in this article seem somewhat odd. Where I live, "cities" are definitely expanding in area, too, if you include "suburbs" as parts of the cities. Much rural land is now converted not just to "residential" and "commercial", but also multiple story apartments and multi-story professional buildings. Everything seems to be getting built taller, with the tallest being (mostly) in the centers of cities. Long ago around here, a very tall residential building was built in the midst of rural and natural lands, and it sparked a legal battle and zoning changes, both on aesthetic grounds and privacy issues, related to the "views" in both directions.
This article then ends with a rather flimsy statement about the effects of dense city centers on the global environment. Mainly:
""It has consequences for greenhouse gas emissions, from both structures themselves and transportation infrastructure around that in order to get people to live there or work there."
But, there is no logical argument that putting the same number of people into more low-rise suburban environments would somehow lower CO2 emissions or decrease other environmental disruptions. In fact, the article does not actually say that the cities' impacts are worse than the alternatives - it just seems to be implied by the closing sentence.
I suspect that any comprehensive analysis would show that the total of detrimental effects on the natural environment from expanding human population would be minimized by accommodating them into existing city areas with increased vertical development, rather than into increased area with unchanged vertical dimension limits.
Just the emissions from personal transportation would seem to make that effect clear. But, there are many efficiencies involved, as well as some losses of efficiency. For instance, heating energy demands are much lower in winter, while cooling demands in summer are much higher in cities, even in winter.
But, the real issue is probably going to be what happens to cities that were designed primarily for cold winters when the climate changes enough that their biggest challenge will be from hot summers?
Hot cities do change the local weather, too. Where I live, the local rainfall is reduced because we are generally down-wind from a large urban heat island. "Fronts" with rainfall that pass over the city usually develop a hole with little or no rain in that part of the front when it reaches our location. On the upwind side, storms are often more severe.