Meaning and usage of "Queens rules"

It's Queensberry Rules...

a code of generally accepted rules in the sport of boxing. They were named so because John Douglas, 9th Marquess of Queensberry publicly endorsed the code.

The term is often used (usually, but not always facetiously) in more general contexts. It normally has the general sense of "We agree to settle our differences in a gentlemanly fashion", but arguably in OP's exact context it has the more specific sense of...

"We agree to take turns throwing a punch (making a point in a debate), then allowing the other contestant to parry that point (rebut it by reasoned argument) before he makes his next point."