They are there by the invitation of the host countries, not to subjugate them and ensure their allegiance to the US. But as the article by Dr. Petrov points out, all empires extract a tax or tribute from the subjugated. Where is the tax or tribute? The fact that oil is priced in dollars does not make it a "tax" as the article claims.
Empire:
"A political unit having an extensive territory or comprising a number of territories or nations and ruled by a single supreme authority."
http://dictionary.reference.com/search?q=empire
Sorry, the USA does not fit this definition. The fact that we have military forces in Japan and the UK does not mean that we rule Japan and the UK.
Correction -- they are there either as a result of our own will, or at the "invitation" of a government that may or may not even reflect the will of its own people (Pakistan, for example). It's also worth noting that the term "empire" does not necessarily indicate hostile intent on the part of the imperial power.
The fact that oil is priced in dollars does not make it a "tax" as the article claims.
But the fact that all U.S. trade is conducted with U.S. dollars does, in a sense. That's his point.