From your article link
If the counter offer is issued by the seller, the buyer can simply accept the counter and deliver it back to the party designated to receive it.
we did that .........Why is our acceptance not a contract?
We wrote a home buy offer to sellers agent, Sellers agent countered verbally with a final full price counter offer. We wrote and delivered the acceptance of those terms to the sellers agent. Then the seller accepted a different offer a week later. Why is our acceptance not a contract?