That's the irony of brands in the modern era. In a commodified market, where all services or products are virtually interchangeable, you either compete on price -- a race to the bottom with ever-declining margins -- or you move upmarket by competing on prestige and perception. Amex's prestige hasn't fundamentally changed how valuable the card is to hold, but it's signed up customers in the first place, and it's signed up an affluent segment of customer. (See: the article's note about the Amex customer's average spend vs. that of other cards.)
But brand relies to some degree on information asymmetry. As a consumer, you assume that a prestigious brand is somehow better, and to whatever degree your assumption is based on pure speculation, the stronger you buy into that assumption. These days, information is widely available at a moment's lookup. You can compare as never before, across as many scenarios as you like. Interchangeable services, like credit cards, are revealed for what they are. Couple this with the fact that cards are becoming a means to an end, and no longer the physical payment mechanism they once were, and the prestige and mystique of a certain color of plastic fades even faster.
These days, the benefits of holding one card over another can be reduced in seconds to a rough mathematical function. How many vendors accept this card? What are the annual fees? What are the interest rates? What is the expected value of the fringe benefits? Amex pioneered the loyalty card ("affinity card," to use the article's parlance) as a means of locking in better fringe benefits. But now everyone's got a loyalty card, and partners in the travel and retail sectors have deals with almost everyone.