The 'RealTime Web' may be a name we are stuck with, but it is still a misleading one. Real-time software is a well-defined field where computing has to complete or fail cleanly by a deadline, because latency is paramount. A two-way phone conversation is an example - if the delay between parties exceeds a few hundred milliseconds, normal conversation becomes impossible, and people have to formally take turns. This is because a true verbal conversation is a flow state, where you are both engaged and responding.
With text, the latency requirement can be relaxed - historically conversations have been conducted by exchanges of letters with latencies in weeks. What's happening is that all kinds of media are having their latency domains expanded.
Technological constraints used to make buffering audio or video prohibitively expensive, so they only domain they could work in was real time, hence Telephony's interruptive call model, and Radio and Television's 'one way to many people at once' model. As storage has got cheap and ubiquitous, these give way to answerphones, TiVo's, iPods and YouTube.
At the same time, the latency of text has been moving the other way, from newspapers' and mail's daily cycles, to hours for webpages, minutes for blogs down to seconds for SMS, Twitter, Facebook and other activity streams. However, as audio and video have added persistence, text hasn't lost it - we do have the ability to review and catch up with the past of our flows, or to re-point people to older points in time, as well as marking out times in the future.
Text's natural parallelism means we are seeing new kinds of public flow states that we have become used to as private ones - hence the "Twitter is public IM" explanation; but the other addition needed to make this stable and not a cacophony is the semi-overlapping publics that mean we don't all see the same flow, but that it is mediated by the people we choose to pay attention to.
Much of the supposed 'Real-Time' web is enabled by the relaxation of realtime constraints in favour of the 'eventually consistent' model of data propagation. Google Wave, for example, enables simultaneous editing by relaxing the 'one person can edit at a time' rule in favour of reconciling simultaneous edits smoothly.
"Real-time" is actually a bit of a misnomer. Most of this activity doesn't truly occur in real time, the way talking on the phone does, and social gestures such as sharing links with friends are just as important a part of the appeal as immediacy
Instead, we should think about a web that flows past, a web where the flow is important, as well as its past. The Flow Past web.