The word real-time has more than one meaning. This is about real-time chat, where the message is expected to be read immediately, as opposed to something like email where the message is expected to sit in a buffer for a while before being read.

You wouldn't ask for the deadlines of a video game speedrunner talking about "real time", either. That means real wall-clock time rather than time displayed by the video game (differences can arise due to e.g. pausing)