I have seen numerous people argue and flood the chat with completely useless clutter for 10+ minutes in a row but they don't get punished, warned or muted because there simply isnt any rule against it. This is by no means to disrespect staff for not muting them for it as it's simply not their fault, however I do think that you should get punished for just cluttering public chat with useless arguing for long periods of time.
There is actually a rule against arguing in chat. You can see it in the rules in Severity 1 Chat Offences. There is a warning required before a mute is issued. You can also make a chatreport of the players who are arguing. Sometimes it's kind of difficult to know if something is friendly beefing or actual arguing, and small arguments are also allowed. When things get heated though, or when the conversation is very long and disturbs the chat, it is punishable. Another thing to note is that since arguing usually happens with multiple messages, reporting this with chatreports is a better alternative than on the forums with screenshots. Chatreports show the last 10 minutes of the player's commands and messages, while screenshots might only show a small portion. The more messages there are, the easier it is to tell if it's a friendly beefing session or something worse. :D
Actually, the rule clearly states that it's only arguing against staff members and not regular members. Was that an unintentional typo?
The rules state "Constant arguing in public chat or in private messages to a staff member.", meaning any and all constant arguing in public chat regardless of who with is punishable. They also include the "-or in private messages to a staff member", because if you argue in a non-staff's DMs then it's completely fine because it's not disturbing the rest of the server and you can just end it via /ignore <username> (this acts as a "block" so you can't receive /msgs from them nor see their messages in chat), however, staff can't /ignore players, so constantly arguing with one in their /msg would result in a punishment under this rule.