There's an important factor that is ignored by the article and it is a fundamental principle in finance. That principle is risk.
Any time anyone asks a question in finance the correct answer is always, "It depends".
Absolute answers like always pay highest interest card make sense mathematically in certain cases but they are not the whole story and don't take into account other factors that are equally if not more important than paying the least amount of interest.
Another factor to consider is cash flow.
If you are someone that lives paycheck to paycheck and can pay off a card or loan sooner to create some additional cash flow that has major benefits for increasing cash flow, peace of mind, and providing a buffer for unexpected expenses.
It lowers the risk of default and late payment fees / increased rates if you have more cash flow. Ultimately leading to paying less in interest and fees.
If there are unexpected expenses you will be glad to have the available cash. That's worth paying a little more interest in the long run.
There's also the fact that it may not make sense to pay down low interest rates like a 4% fixed mortgage when you can invest at rates higher that. In that case you want to pay it off as little as possible and maybe even take out equity to put into investments.