How do I extract seismic amplitude on an interpreted horizon?
The answer to most of your questions is: it depends.
Is amplitude good for mapping channels?
Amplitude maps can be great for finding and interpreting channel systems. It depends on the geology and on the seismic data's characteristics. Sometimes you can just see the channels, which might be qualitatively useful, and sometimes you can infer quantitative information, such as width, thickness, composition, porosity, or fluid content. It depends.
Here's a workflow for any kind of attribute analysis. I'll try to add to it in the next day or two.
When should I use RMS amplitude?
Before confusing yourself with what others do (they are not necessarily a good guide), it's worth reading about different kinds of average.
The main feature of the RMS average, for geophysicists anyway, is that it works on zero-mean data like seismic:

So it's not really that &quot;when using RMS amplitude one must integrate over a window&quot;, more that if you want to measure amplitude over a window, you must use RMS.
Because the values are squared, RMS has two other features (or bugs, depending on your point of view): large values are emphasized, and noise may therefore be emphasized.
An alternative is to use the envelope of the trace (sometimes also called 'energy' or 'absolute amplitude'), which is the magnitude of the Hilbert transform (also called 'complex trace'). It is always positive and has the added benefit of being phase-independent. Read more about envelope..
Which window to use?
Let the expected geology and basic geophysics and statistics guide all of your decisions. Use a window that captures the interval of interest (look at the wells!) without too much non-interesting stratigraphy. But use a big enough window that you don't see a lot of artifacts from large amplitude values coming in and out of the window (this also depends on the quality of the horizons and smoothness of the geology).
Windows don't have to be symmetrical about a horizon. It depends where the features you're interested in are. In my experience, stratigraphic windows are often useful — from one horizon to the next. If you're interested in the horizon itself, consider just using its amplitude directly. If it's too noisy, try improving the pick or smoothing the amplitude map, before confusing things by throwing more geology in there.
What does that caption mean?
Who knows what that caption means? Vague captions plague the geophysics literature. Don't be part of the problem! If only for the sake of your future self, record the exact statistic and its parameters on every image — even put it all in the filename.
Remember what you're trying to do
You're trying to relate the seismic to reservoir properties you care about. This means proving that the property is related to the seismic in as quantitative way as possible. A nice way to do this is to crossplot the property with the seismic attribute — that way you also know the error of the estimate. A map showing wiggly channels is interesting, but nowhere near enough.
I tend not to believe attribute analyses that don't include a crossplot.