Kechol dinei hatorah is very obvious — the right of a property owner to forbid others to derive benefit from his property.
And that also answers the question of whether this has teeth. By making this proclamation, any mosser, whether they know about him or not, who uses their facilities in any way, is a rosho and Hashem will punish him. If he at least pretends to himself to be an observant Jew, he will refrain of his own accord from using their facilities, just as he refrains from eating pork.
Ubiq, you are correct that R Chaim did say that those who ignore the guidelines, relying solely on Divine protection, are rodfim, but that is in the context of the previous question which was about those who break quarantine. Everyone knows that when you conduct a poll the order of the questions matters, and previous questions set the context for later ones. Respondents’ answers to later questions are influenced by the previous ones. So having first been asked about those who knowingly break quarantine, R Chaim’s mind was still in that context.
Even without that, there is a huge difference between someone who has made his own decision that what he is doing is not endangering anyone, and someone who merely says “Hashem will protect me”. It’s obvious that the latter is acting with complete hefkerus, and can therefore justly be called a rodef, while the former simply has a different opinion on the risks involved, which in hindsight can be said to have been proven correct.