These are compelling arguments, but I wonder if the author is focusing too much on language rather than freedom. It is easy to conflate the two since English speaking people are generally the most free, but I think a closer correlation to prosperity can be found by studying the correlation with economic freedom. As far as military alliances go, it's true that the alliances tend to be among English speaking countries, but again, these countries also happen to be free. When is the last time two free countries were on opposite sides in a shooting war?
Now this is a most excellent question!
Perhaps they're intertwined. By that I mean, it's been the English speaking peoples who have, nurtured and exported freedom, in both socio, economic and political terms.
If Rome had used it mighty empire to do as much, the author might have titled his book "A History of the Latin-Speaking Peoples Since 0001" (only in Latin of course) or some such.
Of course Rome, and Greece and many others that came before the rise of Britain And America, were only precursors to what was to come. They had some pieces to the puzzle, but not the whole.
It took a while to analyze those classical civilizations to come up with what we have now. Fortunately our fore fathers had a very good classical education.
In another thousand years....