This summary is not the rule. The rule text controls.
This rule says that the same rules for dismissing a lawsuit also apply when someone wants to dismiss a counterclaim, cross-claim, or third-party claim. These are claims that get added into a case beyond the original lawsuit, like when a defendant sues someone else back, or brings in another party.
If a person wants to drop one of these claims on their own, without needing the court's permission or the other side's agreement, they have to do it early. Specifically, they need to file the dismissal before the other side responds to the claim in writing. If the other side hasn't filed a response, the person can still drop the claim on their own up until evidence starts getting presented at trial or a hearing.
Basically, this gives people a window to back out of a claim they added to the case, but only if they act before things move too far along. Once the other side has responded, or once the trial has started bringing in evidence, dropping the claim usually requires either the other side's agreement or the court's approval.