And a gentleman's agreement would be broken and "resolved" through the gentlemanly art of fisticuffs ­— in other words, it really hinges on mutual threat of violence rather than on mutual recognition of benefit?

No. The agreement is based on the mutual recognition of benefit. The expectation that each will honor the agreement if made relies on the threat of mutual violence. If there wasn't an expectation of benefit they would not enter into an agreement. (The agreement obliges them to either do something or experience negative consequences so if the agreement offered no expectation of benefit to compensate it would be a bad decision.)