I heard the same podcast and the argument is actually the same as this line from the article:

"“One type of writing hasn’t replaced the other,” McCulloch writes, taking care to emphasize that the situation between formal language and internet language isn’t zero-sum."

It's just that The Economist made this division much more explicit, and used it as the basis for their argument while the NYT relegates it to a single line at the end of the article...

There are online forces that prevent language change. It's easier now than ever to have access to the language produced by vast numbers of ordinary people and to police it.

It's also easier now than ever to self-correct. For instance you can use a search engine to find the proper term for anything imaginable, so there is no need to introduce unnecessary words. (Most people who introduce new words do so because their vocabulary and access to material is lacking, not because they have invented or discovering something as of yet unnamed by anyone.)

People participating in online forums are now more keenly aware than ever of their own dialect, because they have ready access to large numbers of people from other regions. I think this will have the effect of globalizing language, through the expunging of unnecessary words in local dialects.