Since "implies that the site is somehow automatically identifying where the virus is" is obviously impossible with current tech & infrastructure, the next most "real-time" interpretation is that it has the most up-to-date data as it becomes available... which it basically does AFAIK, assuming it automatically pulls from its data sources, such as the WHO situation report feed.
It's not impossible, most countries have digitized medical records. It wouldn't be technically difficult to automatically send out a ping to a centralized location when a new patient is diagnosed with novel coronovirus. Politically, on the other hand, it's not going to happen.
I don't think that's the case, it is a map of data updated by an editor. The website in question doesn't seem to fetch data automatically as the sources are making it available.
What would you recommend calling it instead?