The problem is that one of the (most commonly accepted, if not official) meanings of "real-time" is a system that guarantees response within a specific time period. Usually this is a pretty small time period. So also using the term to refer to systems where there is actually no limit on the response time creates a problem.
If we allow "real-time" to be used to represent anything interactive, then how can we make clear when we're actually talking about a real-time system? Really real-time? Legit real-time?
I mean, even though I've never done real-time programming and probably never will, I don't treat the term as up for grabs. I like that I know what "real-time" means when I hear it, so I (e.g.) gently steer coworkers towards different terminology every time they try to label something we do "real time."
Or you could cut to the chase and call it "websockets." socket.io supports other technologies for ancient browsers, but that's a detail that could be addressed in the post.
Our technical terms to some extent do need to be gate-kept against having their meanings watered down, but I've seen so many "realtime" browser projects, that I'm afraid we have to accept it has entered into the common vernacular like "serverless" has, in spite of the inaccuracies.