The article (particularly the linked tweet) somewhat addresses your point: Amex and Discover may offer a superficial degree of competition for consumers, but banks have to obey Mastercard and Visa's rules even when it comes to offering bank accounts to merchants, otherwise they (and therefore all their other account holders) can't participate in the 80% of card transactions that are on the Mastercard and Visa networks.
If you're a bank who wants their business customers to receive payment via Mastercard, you are not allowed to give a bank account to or otherwise handle payments for anyone on the MATCH list, otherwise Mastercard will shut off your bank's access to their network completely, probably putting you out of business. There is little transparency about how entities end up on this MATCH list. The article does not propose an exact regulation, but the end goal would be that a single company can't arbitrarily shut people out of most of the financial system.