The view update part was the most confusing, but I tried to understand it this way:
Imagine you had a magical game engine that rendered the entire world perfectly accurately for every point in space and direction a viewer could possibly be looking at. All you had to do was say:
RenderGameFrameForEveryPossiblePoint();
... // Who knows how much time
viewerPosition = QuicklyGetViewerPosition();
TellTheGPUToShowWorldAccordingTo(viewerPosition);
Well then, you could postpone calling those last two functions until the absolute last minute. This way you have very little or no movement of the viewer's head between when you read their position and when you show the view for that position.
But naturally, RenderGameFrameForEveryPossiblePoint() is slightly out of bounds of current technology. A lot of what Carmack was discussing, as I understood it, was simulating this effect as closely as possible. The way to do that, it seems, is:
StartRenderingGameFrameAccordingTo(lastViewerPosition);
... // Stuff
viewerPosition = QuicklyGetViewerPosition();
viewMatrix = ComputeViewMatrixDelta(lastViewerPosition, viewerPosition);
FinalizeGPUFrameRenderWithNewViewMatrix(viewMatrix);
That final bit is just a perspective transformation of a bunch of rendering that was already computed and given to the GPU. But if the viewer moves too quickly, you can easily move somewhere in the world that wasn't actually rendered, or your perspective could shift such that and object that was once occluded is now visible, or vice versa. It seems a lot of the complexity is there.
The last thing he talked about, time warping, seems to be a similar thing only it's scanline by scanline. So in effect you're saying "hey, video card and display, I know you're going to force me to draw a whole frame at once, so I'm going to give you a frame where each scanline gets rendered a little bit into the future according to where the player is moving."
The effect on a monitor would probably look like a forward shear, but on an HMD (if done correctly), it would correct for the natural shear caused by having to "freeze frame" the viewer's perspective for one entire frame instead of just a scanline.
Some of this may be woefully incorrect, but it was how I explained it to myself. Please correct anything that's wrong or overly simplified.