I imagine this article will be extremely influential among the masses of New York Times readers. The basic problem with the theory that the bigger are the markets, the more superstars will make, and this accounts for the dramatic rise in inequality in the US since 1980 is that it does not fit the data at all for other time periods or other countries, unless one is very selective with said countries and eras.
The article starts out with the stories about how, with television, the Yankees pay their players more because the potential market is bigger. OK, TV audiences are probably much larger than the 1970s, but let's apply the same logic to ticket prices. New York has roughly the same population in 2010 as it did in 1970. The highest priced ticket in 1970 was just $22 in today's dollars, adjusted for inflation. Today, the highest-priced ticket is $2,625. Again, that clearly has nothing to do with larger markets. And the increase in the most expensive ticket unfortunately "over-explains" the increases in players' salary, who haven't experienced 100+ fold salary increases.
Inequality was bad in the 1920s. After the New Deal, inequality was basically unchanged until the 1980s, despite the fact that corporations, profits, and big media, television, et. al. and company's market capitalization were much larger in 1970 than in 1933. Second problem is that Japan's economy grew like wildfire from 1946 to 1992, and nothing special happened to inequality. Mainland Europe and Korea also do not fit the pattern. Canada, Australia, New Zealand and the UK basically only fit the model for some time periods -- i.e., since 1980 for New Zealand and the UK (Reagan-Thatcher revolution), Canada and Australia only more recently.
Thinking of writing your thesis on this? Well, there's already a Temin paper which basically explains all of this, and showing that institutional factors were largely at play. And yet, the "Superstar Effect" is still one of those zombie ideas that won't die... Mind you, it's not to say that I disagree with the notion that as a company's market size increases, it's likely to pay the CEO or top performing workers more, holding everything else constant. It's just that everything else hasn't been held constant in these studies which generally have as data one observation -- the US experience since 1980.
Update: The Temin "Treaty of Detroit" paper is here . Unions, taxes, and the minimum wage were are clearly three big institutional factors which changed around 1980.