As background to my message cited in the question, I said this earlier in the same conversation:
No one has a monopoly on this room but when multiple people ask if you not perhaps want to take your conversations about a specific topic to another room I'd kindly ask you to consider that.
This already answers the question posed here: No one has a monopoly on the main chat room, or the absolute right to restrict the topics discussed there as long as they do not inherently run afoul of the Be Nice policy. We had a rather lengthy discussion about this related to this meta post, where in the end we decided that the moderators also will not restrict the topics discussed for any other reason.
Nevertheless, the point I wanted to make in those messages is different: Because of the shared nature of the room, not only does a single person not get to restrict the topic, but also the people present should try to work out a way in which they all can use the room. This, of course, requires compromise - if a lengthy conversation between a small subset of users disturbs the others, and they express their wish those users take it elsewhere, then the courteous thing to do is to take it elsewhere. Creating a new room costs you nothing (provided you have 100 reputation) and clearly resolves all the tension instantly. I'm not saying one is obligated to do that, but I expect that there will at least be a reasonable and civil conversation about the refusal to do so.
If there are good reasons to keep the conversation in the room (e.g. it's of potential interest to a large set of other users or directly related to site policy or other matters of relevance to the physics.SE community as such), then one should talk about that and ideally the users disturbed by the conservation should show some insight and acquiesce. If it seems that some users are frivolously or one-sidedly requesting conversations to be moved on spurious grounds, one may also talk about that.
None of this happened in this instance. The main response was "just ignore us if you don't like the topic", which clearly ignores the shared nature of the room, and the conversation, instead of trying to find a consensus or compromise, quickly degenerated into mutual attacks and unconstructive comments. This is not desirable behaviour and basically spoils the room's atmosphere for everyone, which is in no one's interest.
It's a chat room, talk to each other, figure out a way to coexist. Merely insisting on others keeping their conversation out of a room without compromise or explanation is not constructive, and neither is insisting others just have to live with whatever you decide to fill the room with. This is not an issue hard-coded rules could satisfactorily resolve, so there are none.