Yes, it has a specific meaning in computer science, but it also has a plain-English meaning, as well as different specific meanings in other domains. For example, in gaming "real-time" means "not turn-based", which I think is close to what web developers mean when they use it for web pages that do two-way interactive communication.
But the term has a very specific technical meaning , not just 'very fast'. This is analogous to when people say that 'NP-complete' is synonymous with 'very hard'. If I posted a problem to HN that I solved and that I found very difficult, but was not np-complete, and said "look at my solution to this np-complete problem" people would certainly (hopefully) complain.
Didn't you lose this battle back when the original Warcraft came out, seventeen years ago or so? Real time is not a technical term anymore in most of the conversations where it appears; it's popular jargon and it means "the opposite of turn-based".
However, I wish you and L'Académie Française the best of luck. ;)