Yes, there is something to be said for this argument. Debit card and cash users pay slightly higher prices than they might otherwise, which do subsidize the rewards of credit card users. But this is distinct from the argument presented in the article, which is that poor people's credit card debt funds rich people's airline miles.
But there factors that counteract this. Merchants pay different average fees depending on the mix of cards that they accept. A dollar store probably sees fewer Chase Sapphire Reserved or Amex Platinum cards than a Gucci store does. Accordingly, the average interchange fee they pay is probably lower. [0]
Also fee surcharging is becoming more common in the US these days, and is already common is some other countries. Visa et al. still don't allow merchants to pass on the actual interchange they'll pay, but merchants can charge a fee to credit card transactions that they don't on debit or cash.
But my original point is that giving rich people credit card rewards are not a transfer from the poor to the rich. It's a rational business decision by card companies that does not require any outside funding source, from poor people or otherwise, to make work financially.
0: There are some other factors that complicate this, such as the risk profile of the business. Riskier generally means higher fees.