Whether you believe the accusation that the U.S. promotes these uprisings or not isn't the most important point. It is a fact that some actors in the U.S. definitely promote these uprisings, but they don't appear to be associated with the U.S. government. Regardless, what I think we need to focus on is this:

“The Russians, by announcing this new doctrine in such clear terms, are announcing their intent to counter this activity [of destabilizing governments by popular uprising] by conducting additional research and analysis, ultimately coming out with counter policies,” he said.
What are the implications of this? Are we going to see a new type of confrontation between the U.S. and the USSR (oops I mean Russia), where Russia is engages states and the US engages populaces? Obviously the Russians desire to limit and even turn back the scale of U.S. influence globally, as does China. Will they form a coalition? Should the U.S. defense strategy change based on this?