Don't understand that you mean here, as Java is both the language and Java VM.

I meant Java, the language. The reason being I took you to mean something like Microsoft announced they were going to do years ago [probably using Internet Explorer]: They announced that web pages were going to look more like computer programs. That was poorly timed because, implying some sort of vendor lock-in using Microsoft products, they failed to foresee phones, tablets and the decreasing relevance of the user's OS.

At the time, I imagine there would have been binary info being exchanged and an enhanced user experience. It would all have had to be either windows-based or something sitting on top of the user's Windows, Mac or Linux OS.

That's why I took you to be suggesting something like Java. Not specifically Java Virtual Machine (JVM), now known as is JRE (Java Runtime Environment). Although applets do things which resemble what Microsoft was talking about, I would point to something more sophisticated like the Open Office Suite as an idea of what websites might be able to resemble.

And no server has no business here, but it also executes byte code, just different.

Sorry, I don't understand this at all. Maybe a flow-chart is needed

[Edit] I just looked very briefly at parts of the Davlik Virtual Machine video (on my slow, expensive 3G connection). I pretty much get the idea, my impressions above are confirmed but I will not know until I can view the whole thing somewhere.